If you have an uncut 340 and the bores clean-up at .020 you wind up with a standard 4.06" bore which has lots and lots more piston and ring pack choices readily available. Plus you get to save the block for additional incremental bores later...If I can I go 4.06 I will and I'll save for a possible need for 4.07 down the road.

Valve shrouding is IMO more of a concern on Big block Mopar Wedges than on small blocks due the SB superior valve angle, on-center valve/bore placement, the limiting factor on SBM's is generally port cross section and pushrod pinch shrouding.

all else being equal a 340 stroker will have a bit less frictional losses at the mains due to its' smaller bearing diameter....a 360 will also be a bit heavier due to those thicker crank mains (steel is heavier than cast iron)

360s are a lot more plentiful though

As for why mopar went to a 360 instead of just a 4" bore 318 block, I suspect cost cutting with the longer 3.58 stroke allowed for cheaper but still strong cast crank production and external balancing saving millions ofver the mass production multi-year run of the engine. As evidence of that, (to my knowledge) there was never a steel or internally balanced 360 made. The 360 was also intended as a gap bridger for trucks and the big C bodys between the 318 and the (was 383, now 400).