I know there is no way for me to type this without it sounding pro BowTech anti Mathews but I will give you my take on the differences, and let me preface this by saying that I LIKE Mathews bows, they are a high quality piece of equipment and there are plenty of models that I wouldn't kick out of bed for eating crackers.
I choose to shoot BowTech because I like them better.........simple as that. I like Mathews bows just fine, I just find more to offer in the BowTech line-up.
The differences shooting them? Depends upon what bow you are shooting? A BowTech BKII vs a Mathews Legacy? A Mathews Q2XL vs. a Mighty Mite?
Some are smoother, some are faster, some more recoil free, some definitely quieter........the bottom line is that they are ALL quality bows!! Aren't the "Bow Wars" about the stupidest thing you ever listened to?

BowTech uses modular cam systems on all of their bows. Mathews uses A single draw length specific cam. Each offer advantages.....I'd rather play with mods than new cams though.
Speaking of cams, Mathews has pretty much backed themselves into a single cam corner with their advertising campaign. They have some very nice shooting quality bows but they are locked into one idea for life unless they wish to look foolish. How far a single cam bow can be refined? I guess they are going to try.

BowTech offers at present 4 different cam systems, from Dual to Wheel to large smooth and small fast singles. All offering different things. I had a very hard time picking a 2004 BowTech from their line-up because quite a few bows offered something very different that appealed to me, going by the Mathews line-up for 2003 I didn't see as much variety and choosing would have been very easy, between 2 maybe 3 models at most.

I've owned Mathews bows so I am qualified to say that BowTechs stock string cable offerings since 2001 have been FAR superior to the factory Mathews offerings.

Without starting a VFT /parallel limb angle war.......BowTech did have the Patriot with its significantly swept back limb angles and VFT benefits months before Mathews did in the Legacy. I think this is where the "Physical" similarities really took off.
And no NEITHER company pioneered this idea, I think we are all VERY well aware of that by now........However I think BowTech was the first to REALLY use it to its full potential.

Actually if you look closely there really isn't a whole lot of apples to apples in specs between the companies......there are some similarities now physically that's for sure with bows like the Legacy and Liberty and I imagine as well with Mathews new Outback and the Justice.

I guess for a while Mathews thing was smooth shooting with respectable speed.......BowTechs was shootability with above average speed.
I definitely think BowTech took a step in the right direction this year by trying to raise the bar of smooth shooting as I think they were missing the boat to a large degree.

Yeah at first glance they seem pretty similar, but the closer you look very quickly they become quite different.