The 70D is absolutely fine with any EF or EF-S mount lens and there will be zero drop in image quality. Canon lenses are not optimized for any particular camera body and work equally well with all. The 70D image quality will be higher than your 600D.
I have a 70D and use it will all my canon lenses from 500mm to 24mm primes and a whole bunch of zooms.
I got mine from ADORAMA. Right now they have a special which includes the 70D body, a 32GB class 10 Sd card, a 3 year extended warranty and a LowePro shoulder bag for $999. The 70D alone is also $999, so make sure you get the kit. Shipping is free. Given that a used 70D is $899, a new one for $999 (Canon currently habe a $200 instant rebate on it) is a good deal and the extra items make it even better.
You can use this link to get to the kit:
Canon EOS 70D kitI really like the 70D. Since I got mine it's become my camera of choice, even over my 7D most of the time.