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Skyrim Walkthrough Part 17: The Blades and the Greybeards (Paarthurnax)
http://www.rarityguide.com/articles/articles/4529/1/Skyrim-Walkthrough-Part-17-The-Blades-and-the-Greybeards-Paarthurnax/Page1.html
By Nick M. Facer
Published on 03/19/2013
 
Now that you've finally resolved that, it's time to go catch a- wait, what was that, Delphine?

Once things are set up for the dragon to be trapped at Whiterun, another issue is ready to rear its head.  If you had the peace talks at High Hrothgar, Delphine will approach you while you’re still there.  If, on the other hand, you didn’t need peace talks, she will have a few words for you next time you talk with her.

The Blades, apparently, have learned something about Paarthurnax.  You can feign innocence, try to be sly, or just agree that he’s a dragon- either way, this is what the Blades know.  Moreover, Delphine and Esbern know that Paarthurnax is a dragon who was once Alduin’s main lieutenant.  While the Blades are perhaps a bit too happy to kill dragons regardless of what they do anyways, Delphine is particularly upset about this and wants Paarthurnax dead- she, Esbern, and any followers you’ve given her as Blades won’t give you Blades quests until then.  While Esbern is not as vicious as her and doesn’t seem to be all that upset, willing to take your word about Paarthurnax’s current inclination, he will still follow her lead (even if it is somewhat regretfully).  Unfortunately, killing Paarthurnax will get a similar response from the Greybeards.

This gives you the quest ‘Paarthurnax’, which will linger around until you choose to complete it, or forever if you don’t.

You can approach Arngeir about this and have a bit of a discussion with him about Paarthurnax and the Blades (he dismisses the Blades as having always been terribly bloodthirsty and thus not the sort of people you ought to be associating with anyhow), at the end of which you can choose to either tell him you’re going to kill Paarthurnax, tell him you haven’t made up your mind, or reassure him that the dragon on the Throat is perfectly safe and you’re not going to make a move against him.

If your only concern is questing, then leave Paarthurnax be until you’ve gotten all the information you can out of the Greybeards and then go kill him.  If you’d rather pick a side, do so now and just stick with it.

Aside from the opportunity to go hunting dragons with the Blades, there’s little to gain from killing Paarthurnax.  Esbern can give you a blessing that lasts five days and gives you a 10% boost in critical chance when hitting dragons, and bringing him a Dragon Scale and Dragon Bone can get a potion out of him that will permanently reduce damage you take from dragons by 10%, but neither of these is terribly game-changing in the end, as you should have been handling dragons before now anyways without too much trouble.  The dragon hunting quests are convenient, but any Blades you converted from followers who aren’t your follower (i.e. tied to your butt with a four-meter string) at the moment can and will die during these fights, and you should be getting randomly assaulted by dragons every so often anyways so it’s doubtful you need the Dragon Bone, Dragon Scales, and Dragon Souls anyhow.

Paarthurnax, meanwhile, will give you your choice of one out of three meditations- Fus, which reduces your stagger by 25% and increases stagger you cause by the same amount; Feim, which improves your health regeneration speed while you’re ethereal (either from a potion or from the Shout for it); and Yol, which grants a 25% boost to the damage dealt by the Fire Breath shout (if you happen to have it).  Fus is probably the most generally useful of these, though depending on how you fight, any of them can be quite good and they, unlike the Blades’ benefits, don’t only apply to fights with dragons.