CPU and Bottlenecking:
This will VARY between games. There's NO exact point where you can say that there's no point in getting a better card. If your Power Supply AND budget supported it then I'd even go as high as an HD7850.
32-bit vs 64-bit:
Don't go beyond 1GB of video memory for 32-bit Windows. I can explain more if needed.
Power Supply:
If concerned, you can link the model number but I suspect it does NOT have any 6-pin PCIe power connectors. Again though, EITHER OF THE CARDS you mention should be fine.
HD7730 vs HD6670:
Get the HD7730 with GDDR5 (not DDR3) video memory. Here's the relative performance:
http://www.tomshardware.com/reviews/radeon-hd-7730-cape-verde-review,3575-7.html
In some games, yes the CPU will bottleneck you so the HD6670 and HD7730 would be closer, but again it VARIES.
HD7730 vs HD6670 for POWER CONSUMPTION:
The HD7000 series uses less power than the previous series. The HD7730 has higher performance. It's possible they use ABOUT THE SAME POWER as a result but I'm guessing.
Summary:
**Bottom line is get the HD7730 with GDDR5 video memory.