The biggest difference between a "weapon" light and handheld is that in a weaponlight, the batteries are "captured", so that recoil doesn't allow the batteries to slam into the spring/reflector/module in the lighthead. Repeated pounding can break components in the lighthead. There's usually a spacer, machined stop or rubber insert that limits the forward movement of the batteries, while still maintaining contact with the spring or contact. Of course, and LED will survive repeated shock better than an incandescent (solid state vs. filament), and weaponlights are usually designed with housings that have built-in accommodations for mounts of some kind.
That being said, there are thousands (or more?) of Surefire 6P's and other handhelds being mounted and used without failure every day. I think the move from incandescent to LED was probably the best improvement for durability, allowing weapon use.
Personally, I'd look for something a little more "utilitarian" than the Quark. All the blinking, flashing, and other "features" are cool, but all you really want (or need) in a weaponlight is enough light to illuminate your target. You can find Surefire 6P's and, as Aimless suggested, Elzettas in your budget range, which are proven lights that many use for weapon mounting. They won't signal aliens to land, but do a good job at lighting crap up.