As far as I know, beyond killing Parthonax, there are no Blades quests. It ends there. They might give you random dragon locations but thats it.
I did not kill Parthonax, his wisdom is sound and after talking to him, my decision was clear. He needs to live. Perhaps if Bethesda decides to throw in an expansion where the questline continues, the choices will be come more viable, but for now they fall flat. No point in killing a wise old dragon.
After the council at the Greybeards between General Tullius and Ulfric Stormcloak Delphine practically runs at me and gives me this quest to slay the dragon. I was a bit pissed simply because i didnt even want this quest in my quest log. I followed Delphine as she was walking out of the Greybeards and when we both ended up outside I shouted her off the mountain. I'm not sure if this does anything to her or not, but i havent seen her since. Good riddance in my opinion.
The Blades quests dont even seem worth the trouble for me. I'm not fond of their armor or weapons (Samurai style) and also for the Blades quests, arent you required to kill other Blades members after recruiting them? I could be wrong on that assumption but I read somewhere that it says something about recruiting more blades members and then having to kill them.
Does no one else play the game to complete it? I mean why not get everything you need from the grey beards and the dragon then kill him just to do the blades quest? I mean thats why I buy video games to finish them not to say oh this characters better than this one so ill forget about this part of the game. Maybe im the only one here that treats it like a game, and a game you play to complete it.