Is a class 2 trailer hitch better than a class 3 trailer hitch?

No.

A class II hitch is rated to 3,500 lbs. A class III may be rated the same, but is often rated at 5,000 lbs or higher.

A class III hitch has a 2" receiver opening which allows you to carry a larger bike rack, cargo rack...

The class II has a 1-1/4" opening which limits it's usefulness for carrying accessories.