I have attended all three, Wesleyan, Nazarene, and UMC. It depends on the indvidual church, I think. I attended a UMC in Florida that was very liberal and contemporary. Jumping up and down loud music, you'd think you were in a Pentecostal church. Then, I've attended a UMC in Indiana that felt almost Episcopal, sleepy and very conservative.
Same with Nazarene and Wesleyan. I've attended a service at Indiana Wesleyan University's Chapel and it was very exciting, then a church service a few miles away, was very conservative and if you said Amen too loud or clapped, you were shushed!!
Just my experience that each individual church is different. But, as a whole, I think UMC is considered the most liberal, then Nazarene and Wesleyan.
God Bless