Will they both work the same when hooked up to an interface? And to a hacked mouse?
Most likely, yes. The circuits usually do two things: adjust the output voltage, and "smooth" the ouput. As long as the voltages are close, you shouldn't worry too much. (If they differ, you might need pull-up or pull-down resisters to even them out.)
The "smoothing" part, OTOH, might show noticable differences. Whether minor or not, that's debateable. The circuits are to prevent jitters and optical sensor "backspin", mostly. FWIW, I can't tell the difference between the older happ green optical boards and the new red boards, but not very accurate testing on my part.
If the TBs were PS/2 TBs, though, you don't need to hack a mouse (and it wouldn't work if you tried). Doesn't look that way, though.