I like both Invision Power Board and XenForo. I've spent years working with IPB forums in the past (since IPB 2.x) and I truly enjoyed managing them along with handling the designs. In fact, my very first forum was created with IPB 2.x and it was a very enjoyable experience for me. Many years later, I still like their software. If I were to create a new forum now, it would be using IP.Board, no doubt.
As for XenForo, it's a great forum software despite being new. It gives off a modern feeling and you can say that it's been coded with great ideas in mind. Now if only they could somehow deal with the lawsuit already and return to developing their own software.