Gothmog is a skilled tactician, but in terms of a duel Azog would annihilate him with his brute strength. I'd go so far as to say that he'd make Lurtz look puny too. "These are Gundabad Wargs! They will outrun you!"
"THESE are Rhosgobel Rabbits! I'd like to see them try...."
He may not appear to be physically capable of defeating Azog but I don't think he'd fight fair anyway. More likely to have a bunch of archers hidden nearby and just point.... pffft... end of problem. Fourth Age Adventures at the Inn of the Burping Troll http://burpingtroll.com
I think Azog would destroy him. He is portrayed in The Hobbit movie as a huge orc; taller and bulkier than any orc. He also is more skilled in one on one combat.
