Lol, I swear.. I like Paarthurnax myself and can see many reasons to side with them, but some of you people who side with him make no sense. It's always the same argument: "I'm the dragonborn biyatch!!" expecting everyone to serve you, else you go on a murderous rampage... Except, the whole point of siding with the Greybeards is that you've chosen to not desire power. Did you not play the game at all or pay attention to any quest dialogue? Did you take a break and walk away whenever Arngier spoke to you?
But you don't "choose" to side with the graybeards unless one considers not doing the main quest to be a choice in regard to what the OP is talking about. But even then it really isn't. If you don't do the MQ and talk to the Graybeards the only interaction you'll ever have with Delphine is at Dragon's Reach when you return the Dragonstone. With Esbern the only interaction you can have is to meander through the Ratway and have him not open the door. So really, you don't get to pick any side because there's not side to pick from.
Once the ultimatum is given to you be the "Blades" they should become non-essential NPCs, thereby giving the player the opportunity to wax two of the three most annoying people in the game.
I put the word Blades in quotation because two fanatic people isn't an organization, it's the beginnings of a drum circle.