My main experience with forum software is with vB, but I am a member at several forums now running XF. I think either XF or IPB would be my choice if I were to start a new forum, and I would likely lean towards XF simply because I have more experience using it.
The more I use xenforo the more I prefer it over other software. My only complaint would be that it's (imo) supposed to be the most modern software, yet it still doesn't have push notifications for mobile
I don't do mobile, so I'm not up on all that, but I think there are third party solutions for that, at least from what I've read at TAZ. I find notifications of any kind to be redundant...if I am engaged with a site, then I am keeping up with what's going on anyway. I know people don't operate like that anymore though.
I think it's a lot easier to use and it has better and cheaper plugins and themes. Only difference is it is mostly German people supporting it and sometimes they don't speak English very well or the English translations are shabby. Also cheaper as a whole. $90 for the forum software. I think it looks better too. My forum uses WBB 4.1. The latest version is 5.0