Correct, The 560 Ti is a bucket faster than the radeon 6770! The AMD equivalent is the Radeon HD 6950 BTW.
If you can live with your 6770 for another month or two I'd strongly suggest waiting until the Radeon HD7870 and 7850 come out. You'll find that they should outperform the 560 Ti and will be cheaper to run power wise and produce less heat!
In the meantime give your 6770 an overclock with MSI afterburner.
BTW what cpu/motherboard are you running? The 560 Ti requires a decent CPU to avoid bottlenecks!