It's a close battle, really. The Dell is slightly faster in terms of GPU power, but the HP will give you the benefits of a quad core. Of course, the quad core has a slower clock than the i5, but the i5 is a dual core. (2 ghz vs 2.5). I would personally go for the HP because the 6770m is a solid GPU and the quad core will help in the long run.
Bad advice, he wants this for gaming, the 7730m walks all over the 6770m for gaming performance, and the i5 has more than performance enough for any games, the GPU will bottleneck first anyway.
If you go for the 6770m you're cutting yourself short and you'll have to use low settings on later games.