BF4 is arguably the only game that benefits from more than 2GB currently.
As for the FUTURE, it's hard to say as the game programming experts have said that they can REDUCE the amount of VRAM needed for the same task. Newer methods of AA, Shared Tile Resources, Tessellation and other techniques can significantly reduce memory usage.
As for the "stuttering" in BF4 by running out of VRAM it's hard to say. BF4 has major coding issues anyway. I played SKYRIM on my HD5870 which had 1GB, then upgraded to a GTX680 and at the same settings my GTX680 was using 1.5GB just for the game itself. Why then did I not get major stutter in Skyrim with my HD5870?
Anyway, it's really going to come down to budget, a Gigabyte 4GB 770 costs $390 or about $50 more than a 2GB version and $60 more than the EVGA 1111MHz card (after rebate). That's a big price difference.
However, at that price you're arguably better off waiting for an R9-290 with a good cooler for about $400 which comes with 4GB of memory as well but gives better performance in games.
The AMD card also has Mantle support, something to consider if "future proofing" as Mantle will succeed though slowly. I don't expect too many games in the next two years though.
There are other features such as NVidia's Shadowplay, G-Sync, PhysX to consider but if they aren't important than the R9-290 is a good bet, again with a CUSTOM COOLER once released.
R9-290 (reference) benchmark:
http://www.guru3d.com/articles_pages/radeon_r9_290_review_benchmarks,19.html
I don't know what the average performance will be compared to a GTX770. Lower than the difference here, but still better.