Udyr is great for climbing.
He's a lot like Jax in that he's a great splitpusher, jungler, toplaner, duelist, hypercarry. Also like Jax, he needs a rework.
Udyr is the definition of a "stat check" champion. You do not win duels with Udyr because you bamboozled them with some awesome combo of spells.
You win because of the sheer amount of stats his abilities give him. You can't miss skills on Udyr, as all of them proc on hit. This is also his greatest weakness, as he is vulnerable to kiting. But even that isn't a huge weakness because of how fast he is.
If Udyr is played well he can easily carry.