Awesome! Well they're in the same general class and price range so not too many huge differences. One is that the Bad Boy has mechanical disc brakes whereas the Quick has the more standard brakes. Both of my bikes have disc brakes. The mountain bike has hydraulic ones which are heaven to me haha. The cross bike has mechanical disc brakes which work fine but are not as nice (force required at the handlebars, modulation ability, etc.). A lot of those features are not as necessary when off trails though in my opinion. The question is whether the standard brakes are better than the mechanical disc brakes and that I don't know the answer to since I've never ridden a decent bike without disc brakes of some kind.
If the disc brakes are more expensive than the other style perhaps the other components on the Quick are nicer to make up for that cost differential. If you ride in mostly nice weather then disc brakes might not really be much of an advantage at all, so it might be worth going with the Quick if that is indeed true about the other components.
I looked at the gear ranges and they are identical so that choice isn't a huge difference either. When I started riding the cross bike I was surprised at how tough it was to go up hills until I got used to it because it's geared differently than the mountain bike that I already had. But in this case they are both similar and offer a pretty wide range of gears including some good low end ones for steep hills.
I think the difference between 8 gears in the rear and 9 isn't big either really (again unless the components are drastically different). I haven't had experience with the specific shifters and derailleurs on those bikes so it might be worth googling a bit to see if there are any drastic differences between them or anything like that. I get really frustrated when the shifting doesn't work nicely (which is partially why I didn't like my old Huffy bike and didn't ride until I got a better bike) so if you might be like that then it might be worth seeing which bike's components are better in that regard. But it's possible that they are both pretty similar which would make sense since they're priced similarly.
Anyway, I'm not sure how much that helped and I am by no means an expert! But it might be some things that are useful for you to think about. Oh, and sometime you might want to upgrade the seat if you start going on long rides. That made all the difference in the world for me along with wearing the dorky shorts haha.
Congratulations on the dog and I hope you have a blast with the bike! Let us know if you have any other questions and maybe I can dig in deeper regarding the components sometime later on if you want me to take a better look at them.