I wasn't impressed with the sword and axe ones, but I am curious about the ignoring armor perks for the mace. Is it just a waste?

All weapon specific perks are mediocre.

Are the mace perks ANY better than the others though? I didn't notice any difference with the other perks at all.

Not really.

If I were to rank them, it'd go something like this: sword, mace, axe.

The axe's bleed is so minimal that it's really not very useful. Maces penetrate armor, so it's really only good against enemies with heavy armor. There aren't that many of them. Swords' crit chance is always useful, but it's not much for the price you pay.

I believe the blunt weapon perks(mace and warhammer) is quite useful, essentially making enemies armor irrelevant. That said one does not need any of the weapontype perks to be effective, they simply give you slight bonuses to a certain weapontype.

This^

Exactly. The reward is just not worth the cost....for any of them. Even the crit chance for the sword. You can put those perks in Enchanting and raise your 1H/2H skill to deal more damage with EACH hit and not worry about a 1 in 5 chance. Plus it will make other enchants stronger as well. That is a lot more useful than any of those skill perks.