Jack, I explained in another thread how single cylinder engines are balanced and how vibration is controlled. Essentially, all single cylinder engines since the earliest days are "half balanced" unless they have either a reciprocating balance weight or use counter-rotating shafts. Half balancing consists simply of increasing the weight of the crankshaft counterweight to include half the weight of the piston, gudgeon pin, and small end of the connecting rod. Both Briggs and Honda use reciprocating weights or counterrotating shafts on their large single cylinder engines but not on their small ones. So on the small Honda and Briggs engines the balancing technology is the same: half-balancing. However Briggs may do it less well in some cases, by using the same crankshaft on engines with the same stroke but different bore diameters and therefore different piston and connecting rod weights, which would make the half-balancing inaccurate. To be fair, though, Briggs is not the only manufacturer to do this: the Honda GXV120 and GXV140 share the same crankshaft, despite having different bore diameters, and therefore most likely, different piston weights, though I haven't weighed them to verify this. They use the same connecting rod, so that is not a source of balancing error.
I am not aware of tilting the cylinder on a single cylinder engine having any effect on engine vibration: I believe it is done to make the engine more compact, not to make it smoother.
One of the things that gives OHV Honda and chonda engines an advantage over side valve Briggs engines, is that they fire every shot: no misfires. Misfires cause a slight torsional vibration of the engine, and also require the throttle to be opened slightly more to compensate for the missed power strokes. However the main advantage the OHV engines have is that they have a much higher compression ratio - typically 8:1 instead of 6:1 - and so have much less cubic capacity for the same power output. The residual vibration produced by a half-balanced engine is proportional to the weight of the piston, gudgeon pin and the small end of the connecting rod, so OHV engines vibrate less than side valve engines simply because a smaller engine is doing the same job.
The outcome of all this is that provided you select an engine of the same power output, an OHV engine will vibrate noticeably less than a side valve engine. Unless they go overboard with commonising crankshafts across their model range, Briggs OHV engines should potentially be as smooth-running as OHV Hondas of the same capacity.