MMA is the ''closest thing'' to a real fight, they don't say it's a real fight, LOL.
Also, if the rules allowed you to knee a down opponent, that change in rules wouldn't be incredibly large difference in MMA.
However, if you allow using even elbows in boxing (not even kicking, just elbow) then that would be an incredibly large difference in Boxing, and that would change EVERYTHING in Boxing.
Boxing is an incredibly limited combat sports.
If I've to give example about how even the elbows alone could change everything in boxing;
Calzaghe knows Roy Jones Jr. can't use his elbows, thus he can get his head this close to Roy like this,
knowing that Roy can't use his elbows to hit him and from this angle Roy can't hurt him with his punches so Calzaghe can do this during a ''boxing match''. This is how technical the Boxing is, it's far away from a real fight.
While MMA is not that limited and even if you remove all the rules, and tell the guys that you can use everything, so they would obviously know they should protect themselves from knees when they were down, so they would take their guards and defense according to that, using knee is already allowed in MMA when you are not down for example.
But boxing? Down or standing, you can't do anything but just punching, you can't even use elbows, thus it's not even close to a real fight.