It would seem that even though the Edolas versions of the People at Fairy Tail dress and act a little differently they share the same basic personality traits with their Earthland versions. Both the Edolas Lucy and regular Lucy were practically in sync. Natsu joke he made about Lucy taking a bath with herself could be considered typical. I think it would be weird to take a bath with someone that looked exactly like me.
Edolas Natsu only shares the personality traits with regular Natsu when he is in a car. I just like how regular Natsu dragged him out of the car and he became somewhat of a pussy.Regular Natsu is not a pussy when it comes to transportation, it is that he just gets motion sickness. He is able to fight it when he needs to. Edolas Natsu just became wimp wen pulled out of his car.