The main difference is that the pilots can overcome "stick pusher" systems used in other aircraft by pulling back on the yoke/stick, though that may be difficult depending on how exactly the system works. (Some use the standard auto-pilot servos, which are relatively easy to overpower, but others make it more difficult.)
MCAS operates by adjusting the horizontal stabilizer trim, which cannot be overcome by the pilot pulling back on the yoke, no matter how much force is applied. In the two noted accidents, the pilots did try countering with opposite trim several times, but as soon as they stopped, MCAS kicked back in to undo their corrections. They did not follow the emergency checklist for runaway stabilizer trim as Boeing/FAA expected, which would have disabled MCAS as a side effect.
There's also a separate problem where MCAS normally uses a single AOA sensor, which goes against aviation engineering principles of having redundant everything. Boeing did offer an optional feature to compare multiple AOA sensors and alert the pilots if they disagreed, but neither of the two accident airlines purchased that option. One of the proposed fixes is to make that a standard feature, both for all new production and mandatory retrofit of all existing planes without it.