I just depends on what you are more comfortable using. And the type of content you will be using it for. Find some demos of each software and try them out. I prefer myBB for customization but I use phpBB when I want simplicity.
Personally, I use phpbb. It is decent, but i am going to be moving to XenForo. I do not have much experience with mybb, but i tried it once and it seemed good.
I am using MyBB for my forum and it is really a very good forum software. MyBb has some good plugins which makes it look more professional forum than PhpBB.
I am also using MyBB and I love this forum software. Its user friendly and very easy to manage. It also comes with some good features like private messaging, reputation system etc. and also have some great plugins which make MyBB better then others
It comes down to personal preference entirely. Try out both and see which suits your requirements best and which feels most comfortable to use. Personally, I prefer MyBB.