I think the lowest-durability ball (GI-SD, for example) might perhaps last two full 18-hole rounds or so. That's just a rough estimate. The cheapest upgraded ball, B-XD, has very high durability, almost comparable to the free ball, if you can compare at all a definite value with one that is endless.
I'd say the effect of buying an upgraded ball should be felt immediately, especially if it's one of the meter-slowdown types (GI-SD, GI2-S, etc.). Or, I remember how difficult it can be to reach Bethpge greens with basic clubs; one of the ultra-distance balls might really make a difference there between reaching GIR or not on quite a few holes.