The two cards are a tossup to me. I've owned both Asus cards and Gigabyte. No issues with either.
The 150W R9-270 is a re-branded HD 7870 that is slightly under clocked. That's why they could get away with a single 6 pin connector, whereas the HD 7870 needed 2. If you want to OC the card, the Asus with its extra 75W 6 pin connector may give you more headroom.
The Phenom II X4 965BE that I have in another machine is running @ 4 GHz with a R9-280 and no bottleneck with any of the games I have tested so far. I can push the 280 to 100% usage. So you will be fine with the 270.