Little would change. Vulcans do little to nothing in TNG. You see Spock and mabey an occasional Vulcan(They couldn't all be on Vulcan, they have colonies). 10,000 survivors makes little sense to me as they are a space faring civilization.
Vulcan may be a founding world of the Federation but there is not much there to write home about.
I think it wouldn't be terribly different in some regards, and much different in others.
First, with the loss of some 40 odd ships to the Narada, the Klingon fleet is probably mostly in shambles. This leads me to the conclusion that Praxis would explode sooner (how much, I cannot be certain) as they try to replenish the lost ships. Following this, the Romulans would either conquer the Klingons, or they would be subsumed into the Federation as some kind of protectorate (like Bajor in DS9).
Also, with the seemingly more militaristic bent the JJprise showed, the Galaxy class explorer ship will probably be skipped in favor of a Sovereign-like ship as early as 2366 (when TNG starts).
However, with Kirk being the captain of the Enterprise as it should be, the general timeline of TOS is theoretically mostly conserved, except that one episode where they go to Vulcan and fight with lirpas. This means it's entirely possible that not much will change.