IMO, Mathews makes an extremely high quality bow. You just look at it and it's put together well and everything appears to be top-of-the-line. Very few, if any, drawbacks or downside to them.
BowTech, on the other hand, is just flat-out better.
j/k (sort of) Seriously, though, in shooting both brands, I thought they were both great. BowTech just felt smoother and seemed to shoot better. I was more impressed with BowTech's "feel". Even shooting my '04 Liberty against the '05 Switchback, I like it just as much. Admittedly, though, part of that may be that I'm very comfortable with my Liberty.
Mathews vs. BowTech, to me, is like a 64 GTO vs. a 64 Olds 4-4-2, or a 69 Charger Daytona vs. 70 Superbird. Very similar, and, to a degree, it comes down to personal preference. Personally, I like both Mathews and BowTech, but I've never cared much for the Hoyts, as their draw doesn't seem as smooth to me. To each his own, though.
Ask around, look around, do some research, etc. But just about everyone will tell you to shoot a bunch of bows and go with what you like best.