Parth is too cool to die.
He could have led in Alduin's original absence, but instead he chose a life of solitude and learning to live with the pain of unsatisfied hunger.
He became a monk of sorts. And he is really adamant in spreading that way to the other dragons.
Killing him isn't going to help dragons evolve their ways.

Paarthurnax has clearly turned over a new leaf and his immortality will make him an invaluable asset in the battle against dragons and possibly the battle for control of Skyrim in years to come. Do not jeopardize this to perpetuate a millennium long enmity.

Which was against the Greybeards' teachings. Notice he's not with the Greybeards anymore, and the Greybeards don't want to take sides in the political struggles (they don't like getting involved in it at all, but do relent for the peace treaty at your behest). Ulfric also never met Paarthurnax.

Delphine is a conniving jerk. She knew the whole time that Paarthurnax was a dragon leading the Greybeards on the Throat of the World, and wanted him dead. She also knew that you were going to meet him to get his help. She confronts you about Paarthurnax after you meet him, learn about the Elder Scroll and Dragonrend from him, get the Elder Scroll, learn Dragonrend, and beat Alduin (with Paarth's help) to chase him into Sovngarde, and you know what she says when you tell her you were surprised to find out he was a dragon? "That's fine. We needed him, now we don't."

That's not justice she's after, that's vengeance or just plain hatred.

He knew of it though. But as he said, it was impossible for him to actually know it. He still told you how and where to learn it.

Parthurnaax is attempting to quell the other Dovah, There is a chance that he and the other Dovah may turn if he's allowed to live. Its a certainty if he's not...

So does Esbern. It depends on how you play it, and where you get your info from. In the end it all leads to the same end + 1 more dragon dead.

Paarthurnax, no contest.

Delphine is an arrogant jerk, who comes closer than she probably realizes to being summarily executed by the very person she's trying to recruit. First she insists that you help her, then she says you can't be trusted, all the while holding back information that will help you decide if she's even worth bothering with in the first place. Paarthurnax, on the other hand, is friendly from the start and doesn't keep secrets, although you do have to prod a bit to get some of the information.

Furthermore, while Delphine is busy being irritating and overbearing, Paarthurnax is instructing you as to how to defeat Alduin. It's true he doesn't actually teach you Dragonrend, but it's highly unlikely you'd ever find the Elder scroll without his help, since your character almost certainly doesn't know about Septimus unless you delayed the main quest.

The icing on the cake comes once you've completed the main quest: rather than expressing gratitude for stopping Alduin, she has the gall to deliver an ultimatum to the very person she's supposedly sworn to serve, the gist of which is "You know that fellow who helped you save Nirn? Yeah, I want you to go kill him now just because I hate him". To add insult to injury, there's no opportunity to royally b*tch her out for being so dense, nor even to tell her to go screw herself, if you're so inclined.

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I am aware that Paarthurnax himself says that he shouldn't be trusted, however he also says that he is going to try to teach the other dragons as he did the Greybeards, so it's worth taking a risk if it means the threat can be abolished permanently. I'm actually more worried about what Odahviing will do, as he's completely opposed to Paarthurnax's 'way of peace'; yes, he's technically sworn to serve me, however he's only doing so under duress as I'm the Dragonborn, so I have a feeling I'm going to have to swat him soon lest he cause a schism amongst the Dov.

She suggests you seek out help from the Greybeard not Pathnx. I think if she had known the leader of the GB is Pathnx, she probably would've set up an assault on the High Hrothgar tower, and forced the info out of Pathnx.

Hahahaha. She and whoever else she brought along would get owned by the Greybeards fus-ro-dah'ing them all the way back down the 7000 steps. Even if some snuck by they could not reach the top of the mountain without dying in the wind. And even if they STILL managed to get all the way up to parth he would simply kill them himself.

So i suppose you as a dovakin have liitle chance against the Greybeards?

Ulfric is involved with the Greybeards, not the other way around. Ulfric chose to use his gift, that the Greybeards taught to him, for a bad(won't say evil) act.

So Ulfric is involved with GB but GB is not incolved with Ulfric?

This is entirely based on the assumption that you would be part of HER assault in the first place. I myself would love to sit back and watch them get butchered. This definitely would be the funniest part of the game.

Well assuming that this would have been the path of the Main quest line if the writers chose it that way, I can't see her sending anyone else but the Dovakin to do the quest.

Then I would be at the same place then as I am right now with the blades, them sitting alone in their tomb and me not caring in the slightest.

The Blades have know for hundreds of years, and she knew where he was. She has http://imperial-library.info/content/atlas-dragons, which explicitly states:
Funny that it neglects to mention him turning against Alduin and the aid he provided in the Dragon War.

I haven't come across this book. Only thing I got was the Map of the dragon tombs. It's more likely that Esbern knew. Besides it states in wikia that this book is located in Sky Haven Temple, & not Riverwood.

Edit: Maybe she knew about it.

Maybe. But they meet up before you meet Paarthurnax.

The Blades are total dumb asses in Skyrim. They have this goofy obsession with killing every dragon in existence, regardless of circumstances.

Me: "Delphine, we've discovered a dragon who rescues drowning puppies and is working on a cure for cancer!"

Delphine: "It is evil and must die!"

It's more likely that they both didn't know, as the dialogue for the quest Pathnx starts along the line of "It has come to our attention that the leader of the GB .......". Unless, they are lying to you.

See this is where I think things go awry, and I lump this right along with the Dunmer and Orcs of Skyrim somehow owing people who weren't even alive when they and/or their ancestors were given sanctuary in Skyrim. How does someone like Ulfric deserve any credit at all for deeds he didn't even do, and why should people that weren't even alive when it happened owe any debt for it either?

This goes along with this too. Talos does not have a direct influence on the Empire and certainly not the Blades. At the very best what you describe is the type of person that is contemptible in the real world: the self-absorbed theocrat that has the audacity to think that THEY dare speak for the being they worship.

Here's the reality of this for me:
You have these two survivors that supposedly are pledged to the Dragonborn. Even the "veteran" was not around anywhere close to the time period of even Oblivion, the most recent game. They are owed nothing in my opinion. They were around for a war that was lost, and then turn around and come back with a kooky plot of genocide. Revenge is something that is always evil, no matter the reason in my opinion. It has been thousands of years since Paarthurnax did anything evil. The lives of Delphine and Esbern combined are drops in a bucket compared to his experience and wisdom. They have the audacity to be judge, jury, and executioner (oh wait no they try to send you for that last part with no input from you whatsover despite the fact they supposedly serve you). Not only that, but they have the audacity that they dare act as if they are official leaders of this new so-called "Blades?" If I were helping rebuild their Blades the organization of dangerous, reckless, morally blind assassins that would result wouldn't deserve to bear the name. They abandoned their right to wear that title the moment they decided to slaughter the innocent and redeemed, as far as my character is concerned. While it's true redemption is objective, beings that have lived a combined total of less than three hundred years have no right to judge the redemption of a being who has lived for thousands of years in peace, I would think.

In many ways the new Blades are just like the Thalmor. Two sides of the same coin, one side pro-Talos and the other against. Much like theocratic battles in the real world where people try to justify atrocities by claiming to act or speak for a divine being, claiming that their enemies are barbarians but they are not due to doing God's will, the Thalmor and the new Blades would be two sides of the very same coin. Enemies that are more alike than different, both contemptible.

Esbern says that, "First The Greybeards protected him THEN THE EMPERORS."

My mouth hung open at that.

Wait, guys, you were ordered not to kill him by the Emperors - the guys you served and have been waiting centuries to kill him anyway?

I ditched any plan of helping rebuild the Blades then.

A what? In that sense Greybeards are more like the Thalmors, who sit there & do nothing while the world is running in to total chaos, just so that they can sit their selfish a_ses on their ideal of Peace. What do they have to sacrifice? Years of meditation & contemplation for peace?

I think that it's very obvious here the "blades" are really the bad guys. Zeopard's words rang very true.

Yeah, well. you can also just sit on your a_se and contemplate & meditate about peace.

That's not how it was for me. After completing the peace treaty, Delphine walks up to me all like "We know about Paarthurnax." I say, "Yeah, turns out he's a dragon." She says "That's fine. We needed his help, now we don't," and proceeds to give me the ultimatum to kill him or lose their support. It definitely implies they knew about him (as does the book in their possession), and they know he helped me.

The Greybeards are pretty explicit that they don't expect you to follow the Way of the Voice, and they'll still teach and guide you in your use of Thu'um because you're Dragonborn. However, you must do what the Blades say, or else, even though you're the leader they've been looking for for guidance.