Yes! You can use all three of these interchangeably.
Just be careful with the last two:
"It looks better on you than it did on me" - (DID - tried it on in the past)This would apply more to something you just tried on once.
"It looks better on you than it does on me" - (DOES - wore in past and probably still wear it often) This would apply more to something you own, or wore more than once and are giving to someone else to wear.