You're opinion on these as gaming devices?

First thing here, when it comes to gaming the only reason to use a laptop is if you travel a lot. Since you have desktops also you are considering, I'm going to ignore the laptop completely, not to mention no OS which puts it above your budget once that's included.
The two desktop builds are very similar in performance overall. The NovaTech Black NTA30 which sports a FX-6300 with an R7-260X vs. the Advent DT3415 sporting a Core i7-3770 with an HD 7770. The 3770 is a slightly better CPU for most games while the R7-270X is a slightly better GPU for most games. You could look at some of the benchmarks for games you want to play and see which performs better for what (I can almost guarantee it will depend upon the game as to which system performs better). One difference of note is that the 260X has 2GB of video ram whereas the HD7770 has 1GB (sometimes that can be a factor)
Personally, I think the NovaTech looks more like a gaming PC than the Advent which, IMO, looks like it came off an HP or Dell shelf but let performance be your guide here


I'd pick the FX6300 with the faster video card over the i7 with the 7770. The i7 is a bit much for the 7770, if you can get the 7770 combined with an i5 for cheaper, that would be a lot better.

The video card in the laptop is usable for gaming, but is slower than in either of the desktops, only get that if you absolutely want a laptop.