Yeah, this question bothers me quite often, as far as I change my phones often as well.
I know for sure that SMS messages are left, so if you are going to give your old phone, you’d rather clear it up.
I had not the best story connected with that: I gave my phone to my BF for a week, naturally I replaced my sim card, BUT I forgot about the left SMS messages there.
So he found out something he’d rather not know at all, and we broke:(
So, Nessa, don’t follow my sad example!