Should I buy the existing 3 GB version or wait some more for the 6 GB version? Or maybe go for a GTX780Ti? FYI, I intend to play games (I mean GTA V PC) at 1080p (higher res monitors are out of the questions for the moment).
If you need a new card now, the 6GB of memory won't hurt but at 1080p you would struggle to fill up even half of that - you could argue it's pointless for you at this moment in time. I would put the money towards the extra power of the 780 Ti, as it averages between an extra 5-10 FPS in most games over the 780, and can easily play any game out today at 2560 x 1440/1600 resolution later if you can upgrade your screen. IMO, It struggles at 4K a bit in titles as the 3GB of video memory becomes an issue from benchmarks I've seen.
Perhaps wait for Maxwell?
If you don't need a new card right now, and can wait, this is probably what I would do. The release is delayed though, but should be out in the last quarter of this year.
Mega Beast - Intel i7 4790K | Gigabyte Z97X-UD3H-BK | 16GB DDR3 | SLI GTX 970 | Samsung 850 Evo 1TB
Mini Beast - Intel C2E QX9770 | Gigabyte X48T-DQ6 | 16GB DDR3 | KFA2 LP GTX 750Ti | Seagate 2TB SSHD