The Titan has a ‘DP’ mode which can be switched on and off for better double precision speed.
All recent GPUs can handle 64 bit calcs, just the Tesla line is oriented towards that kind of work.
Doing memory operations on 64 bit words will be fine on a GTX 780/780ti, but if you are doing large FFTs or Linear Algebra solvers in 64 bit that is where there will be big difference.
Do not mean to make this seem complicated, much depends on what you plan to do with CUDA.
For work projects I use cuBLAS, cuSPARSE,cuFFT and thrust frequently, and for ‘hobby’ projects I tend to write my own kernels (both 32 and 64 bit).
Do they make a 6GB 780 ? I thought they were all 3GB.
The main things I like about the GTX 780ti are the 336 GBs bandwidth and the fast 32-bit integer operations.
If you asked me which GPU is the best all round value for everything, I would say the Titan. If you asked which is best all-round (no price limit) I would say either the Tesla K40 or the Quadro K6000.
For a beginner any newer GPU will be fine, so just get something decent and figure out what projects you are interested in developing.
And if you also play games, then the GTX 780/780ti are going to be awesome in that area as well.
Any person in a computer store is going to evaluate GPUs based on gaming only. It is true most games will not require the full pci-e 3.0 x16 capability, but if you are writing large image processing applications you can push it farther than a typical game.