Shane-
I own both a 1450 and an 1811, which is nearly identical to a 782 except it is newer and has a slightly different engine.
Both QL's and 82's are quality machines. My 1450 is smoother than my 128 at full throttle because of the iso-mounts, but the 782's twin cylinder engine is smoother yet. 82 series tractors generally have more power because of the larger engines. However the KT-17 series I engines in 682's and 782's have a tendency to blow up if not taken care of. A QL will in most cases be more fuel efficient than a 782 or similar; my 1450 burns far less gas mowing the lawn than my 1811.
I like both tractors, but if I had to pick I'd look for an 82 series. The smoothness of the engine is unbeatable. As far as quality goes, the 782's use a rebuildable hydraulic cylinder in the lift, whereas the QL/1x9 cylinders are not. I have not discovered any other real differences in quality yet.