It's obvious that even the design of certain enemies is different. In Lord of the Rings, the trolls were presented as beasts, they didn't talk or have personalities. For the famous troll scene in the hobbit however, it was necessary to have the trolls talk. The trolls features and movements where also much more human.
As the following two instalments of the Hobbit come out, I'll be sure to make a more complete comparison of creatures and characters in the two series.
*Update* A reddit user pointed out something I felt should be shared on this post.
"It is worth noting that in all cases these are different breeds of these races. Thus it's reasonable to assume they'd look slightly different. I saw a behind-the-scenes video a few months ago where PJ says that this was deliberate. The Hobbit vs LotR * Mountain Trolls vs Cave Trolls * Misty Mountain Goblins vs Moria Goblins * Gundabad Wargs vs Mordor Wargs."I think this is a very interesting and plausible explanation for the differences in appearance.