Like the last person said, your question finally got answered in the last episode- Elijah is older.
I didn't want to answer your question until I was sure. but I suspected that Elijah was older, because Klaus had a different biological father, and that guy was killed par Elijah's biological father, so I found it hard to believe that their mother would just continue being married to him and having kids with him, so I suspected that they had had Elijah first.