Get the GDDR5 version, any game that exceeds the 1gb dedicated memory is going to run like crap anyways on a 5670, so hyper memory isn't going to be of any benefit for gaming. For "the new heavy graphic games" I would think you would want something more powerful than either of those cards unless you are on a really tight budget or have a lower resolution screen.
The 6670 is like 25% faster than the 5670, so if it doesn't cost much more then that would be a better choice, but to play on high settings on newer more graphic intensive games I would try and stretch your budget to at least a 5770/6770, and ideally a 6850 or a GTX 460.
For their prices the 6670 and 5670 are both good cards, but you will have to turn down the graphics settings to be able to play alot of games.
What exactly is your budget, and where are you able to shop?