the 7750 is significantly worse than the 6770. Read the benchmarks in this article
It performs worse than a 5770, which is a slightly slower card than the 6770.
Unless energy consumption is a concern (7750 uses very little power) then go with the 6770.
edit: the 6xxx series is only one generation behind and represents a better deal for those on a budget. Until we get some price drops, the 7750 is not worth it.
and asus and gigabyte are both good brands, pick whichever you like. Don't pay extra for either though.