It depends on the situation...
If you bump into someone, you'll probably say "Desculpe", Me desculpe, "Desculpe-me"
However, if you need someone to move or to go to a place, you can say both.
Desculpa/Com licença, Você pode ir no meu quarto e pegar meu shorts?=Excuse me, Can you go to my room and pick up/get my shorts?
Com licença/Desculpe, vim dizer que você fica linda nesse vestido=Excuse me, I come here to say that you look beautiful in that/this dress.
Desculpe/Com licença, você fala inglês?=Excuse me, do you speak English?
(Observation, This is just my experience, other people may use it different from mine) :) any mistakes, you can blame my keyboard....