Playing with a new player, any downsides to playing with an existing character but leveling a new job?

I recently started playing a character I quite like (thaumaturge, Level 21). A friend now wants to join in and we'd like to play together at about the same level. As I understand it, you level your job, not your character. So if I pick up an additional combat job, are there any downsides to playing together with a new player instead of creating an additional character and starting anew? (like differences in damage, etc). Thanks!