The Bear Form has considerably more HP and a melee attack (as well as a few abilities that improve both his and his spirit bear's attack). And still has access to all the abilities the Druid Form Has.
The Druid Form has considerably less HP and a ranged attack. And none of the Bear Form exclusive abilities.
Realistically, the bear form is flat out superior in every way EXCEPT that it's attack is not ranged, so during situations where a ranged attack is absolutly neccesary (attacking from high ground down into the river for example) you would want to be in Druid Form. Or if your trying to have the spirit bear tank for you because the enemy melee heroes have some kind of ZOMG horrid orb that would really ruin your day.
In the end its basically the argument of is there some reason you NEED a ranged attack at this moment?
Interesting after-thought: I don't know if Dota 2 is different when compared with the original DotA mechanics, but I know that some items work differently depending on if they are equipped to a Ranged or Melee hero in the original DotA. I also know that these items only remember the status of the hero at the time of purchase. This opens up all kinds of interesting situations with your ultimate.
IE: Morph into the Bear Form, and buy yourself a Vanguard. Now you can morph freely between ranged or melee form and still have the 'melee' version of the Vanguard. There are many other exploits like this one, but that wasn't the nature of the question so I'll leave it at that.