Mushroom hill is quite different in the beta. First off you start out differently.
The beginning area has been changed drastically to accomidate Knuckles' route above rather than below.
Monitors changed to a bridge here.
Instead of showing a closeup of all the layout differences, here's a map to make it easier:
Beta
Final
Note that Knuckles' route in the lower part is absent in the beta. Instead, his route is moved to the top of the level, to the immediate right of where Sonic starts. It's still about the same length though, and they merge at around the same area.
This is a super ring in the final
In the beta the miniboss's axe hurts you, unlike in the final.
The switch was changed to use Knuckles' pallete instead of Sonic's
No invincibility monitor
Enemy added. Also note the spring not there in the final, and the mushroom not there in the beta
Shield change.
Much of the beginning area has been changed. There's also the addition of some platforms that only Tails can seem to get to. Knuckles' route has also been changed quite a bit.
Beta
Final
This area changed to have a super ring in the final. Knock down the monitors to reveal
Choose wisely.
Boss moved over to the right in the final. This is probably to prevent a bug seen in the beta:
You can just keep hitting the back of the thing forever and the battle won't start until you move to the left and hit the actual satelite.
Additionally, no matter how many times you hit the boss when Robotnik appears, you still need to hit it the full amount of times when the actual battle begins. In the final, hits prior to the battle count for the total.
The boss doesn't explode until he hits the wall in the beta. In the final, he starts exploding once the last hit has been done.