I started my new forum on MyBB, and from using it around a month and a week. I can say its great but 2 things make it a downside from using.
1. The Mybb package has alot of features build in so you don't have to search for mods, because most that you need are already in it. I personally find this bad, thats why phpBB is great. MyBB has to many features build in it, which causes you not being able to make your forum more special or unique then others. As most will have same structure look out if using MyBB. (This is just in short what I mean.) With phpBB you can really go far customizing your site, with MyBB you can do some to but not as much as on phpBB.
2. Cookie problems, this is just from my own expierience. But I find MyBB to be crapy to wards phpBB on case of not having cookie problems. On MyBB I first could not log in, I fixed it, I forgot how could not log in again, other time could not log out, I do an action in ACP I log out, I got to change something, edit a file to be able to log in again, etc ... That mess has taken much time of my hands. Never had that crap on phpBB. (maybe I am a bit unclear but my English isn't that great to explain.)