What will I stand to gain from killing Paarthurnax and getting back in good standing with the Blades?

Here are the advantages/disadvantages as shown on UESP:

If Paarthurnax dies:

• Arngeir retracts the Greybeard’s hospitality, and it is no longer possible to ask him for the locations of Word Walls .
• Paarthurnax will no longer be around to provide meditation bonuses to certain Shouts .
• The Blades will welcome you once again, enabling the completion of Delphine ‘s recruitment quest.
• Esbern will offer to take bones and scales in order to create a potion which grants a powerful permanent bonus to damage versus Dragons (currently, however, the potion is bugged and does nothing).
• The Greybeards will not host a peace treaty, making the Civil War questline mandatory to complete in order to proceed with the Main Quest (if Season Unending has not been completed and the Civil War questline has not already been completed).

If Paarthurnax lives:

• The quest will never disappear from the journal, and the dialogue options concerning the player’s decision will remain for all the characters concerned. (This may be a glitch, as Paarthurnax is labeled essential after the Main Quest is completed). (Edit: Tell the Greybeards you wont kill Paarthurnax to remove from journal. Works sometimes, but not every time.)

• Arngeir will still disclose the location of Word Walls.

• Paarthurnax will still provide meditation bonuses for Shout words.
• Paarthurnax will appear for an extra cutscene after Alduin’s defeat, wherein he details his plans to rein in the Dragons and teach them to live under the Way of the Voice.
• Delphine’s recruitment quest will remain uncompleted.
• Esbern will not offer to create the potion.