The GTX 780 Ti is faster than the GTX 970.
The GTX 970 has more VRAM, but there is no game that currently requires more than this at 1920x1080.
While you find people claiming Battlefield 4 requires more than 3GB, this is only with mantle.
You can see the GTX 780 Ti with 3GB VRAM out-performing the AMD 4GB cards with mantle in this benchmark:
http://www.tomshardware.com/reviews/nvidia-geforce-gtx-980-970-maxwell,3941-8.html
Watch Dogs also requires at least 3GB of VRAM for ultra textures:
http://www.geforce.com/whats-new/guides/watch-dogs-graphics-performance-and-tweaking-guide#textures
There are also two new games coming out that recommend more than this, but they haven't been released yet so the material may not be correct:
http://www.tomshardware.com/news/evil-within-gold-bethesda-horror,27765.html
http://www.overclock.net/t/1515461/ipon-shadow-of-mordor-6gb-of-vram-for-ultra-textures
Note that at 1080p, the value of these very high resolutions textures is questionable.
I think the GTX 780 Ti is a great card and more than enough for 1080p with a 60 Hz monitor.
While the GTX 970 is about 5% slower at stock, it has 4GB of VRAM and support for some new features.
Without over clocking yourself, most cards are factory over clocked anyway, and they can likely get more of an increase from the GTX 970 than the GTX 780 Ti because of the chip design.
Personally, I would choose the GTX 970.
The only older card I would consider in favour of this would be the GTX 780 6GB version as I think the extra VRAM makes it even more future proof.