Slightly off-topic here, but it's quite easy to explain why simply measuring bus width is insufficient for calculating memory bandwidth. All it is is a simple formula.
(Effective clock) * [(Bus Width) / 8] = Memory Bandwidth
or
(Base clock) * [(Bus Width) / 8] * 4= Memory Bandwidth
Quite simple. Base clock being the base memory frequency (1500 mhz for the 650 TI boost) And effective clock being the base clock multiplied by 4 (6ghz for the 650 TI boost) since GDDR5 works much similar to the way DDR3 works, except it's 4 bits per cycle rather than 2. So heres an example for the 650 TI boost;
[1500 * 4] x [[192 / 8]] = 144GB/sec Memory bandwidth
The 650 TI boost is on newer architecture, is more efficient, has DX11.1 (which is just a better optimized version of DX11) and for any of the decent manufacturers, is over $200, and while the 660 is cheaper than a 560TI, both are kind of pushing the envelope imo for the OP's budget range, since he was originally looking at a 7770. If he was going to go in the 200-300 price bracket i'd recommend a 7870xt over a 660 or 560 TI.