340 stroker pistons
Is the block already at .060 or will it be after another bore resurface? If this is a numbers matching block in a car you plan to 100 point restore, I would say keep the 340. If not, why mess with it. You could sell the 340 for more than a running 360 core would cost. Then buy stroker kit, add heads etc... and you're in business. Heck if the 340 is currently running, you won't have to take the car off the road. Besides, the 360's slightly larger main journal makes for a somewhat stronger bottom end.