No SLI planned, and the cost won't affect my decision. The 4gb is cheaper, though..
Well the lightning is faster. Recent games have started using more than 1GB of VRAM. But i don't think there are any games that use more than 2GB VRAM currently. The performance of the GTX 770 will itself become a bottleneck before a game starts using more than 2GB VRAM. Of course if u are doing some rendering stuff then that extra VRAM will be useful. Other than that i think the only major difference i see is a backplate included in lightning
^ you're very outdated then. I have the 680 Lightning, the same thing as the 770 lightning. I can tell you that 2GB is just BARELY cutting it in today's games at maxed settings. After about an hour of gaming in BF4 ultra and with only 2x MSAA for example, I always max out the memory. 4x MSAA gives me low FPS so I naturally keep it down but when it's on I get stuttering on occasion and I imaging it's from the V-RAM making room. Get the 4GB version. It's SO much more future proof. I wouldn't get a modern card any less than 3GB if you want it to last.
Edit: Am I the only one enraged by the fact that the Lightning edition isn't 4GB despite the premium price and for some reason they decided to make a 4GB gaming as well? should be a 2GB gaming edition and a 4GB lightning edition. Am I right?
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.