I don't think either were.

I wouldn't say annoying but I say he's arrogant

Neither are annoying. I like Near and Mello is my favorite character

The only thing that bothers me about Mello is the fact that he cares more about defeating Near in a race of who can catch the culprit first rather than focusing on catching the culprit for justice's (or L's) sake. Because if Mello had decided to put his pride aside and teamed up with Near to catch Kira, his and Matt's deaths could've been avoided.

tbh both, but Near is such a ripoff of L so he really annoys me