I reached level 72 with the gunzerker. If I were to rank Normal, TVHM, and UVHM from easiest to hardest, here's how I'd rank them.
UVHM>>Normal>>>TVHM
The reason I ranked TVHM harder than normal is because the enemies get a lot harder in the 2nd playthrough, and for me it took forever to find solid guns. If you have great guns TVHM should be easier than Normal.
UVHM is by far the easiest because by the time you are ~level 50-60 you will likely have very good weapons and the enemies don't get much more difficult. It was hard, but it gets easier later, with badass guns.
EDIT: Another one of the reasons it likely got easier towards the end is because the gunzerker gets a lot of nice perks and skills near the end, so that's partly why it got easier in the end.
