The beta uses the "SEGA" tune from other Sonic games, rather than the newer one
The title screen shows off that this is (or is an early or later build of) the E3 demo
Special stages use increments of 60 rings in the beta, rather than 50 rings in the final
One of the funnier bits in this game is the use of placeholder images instead of prerendered sequences. They never even bothered to add a Chaos emerald tally screen in this build. Also notice the typo of "Chaos" in the second screenshot. Obviously they spared no expense.
When you finish act 3, it still shows a Flicky, Tails and Knuckles bonus, even though you never encounter any in act 3
If it takes you more than 10 minutes to complete an act, it will show "Too Long" under "Time Taken" in the final. In the beta it just maxes out at "9:59"
Beating the Final boss shows the end of Act 1 screen, rather than the "Sonic got through the Final Fight" screen