I beat the MQ so I have Dragon Call as well as Animal Allegiance, so I can say what I know about them...
I learned that Animal Allegiance only works if animals are around you and you are being attacked. They have to be animals not aligned with anything in particular, if that makes sense. Here's an example: I was fighting some soldiers near a roadside caravan that had an accident. Their horse was the only animal around. I used the shout and their horse glowed slightly but did not move to attack me. I'm not sure if it was because it was aligned with them or domestic animals cannot be called. You'll probably need a wolf or something in the area while you are being attacked by something for it to help you.
Animal Allegiance won't call dragons or get nearby dragons to assist you, either. They are sort of above the animal category. I mean, they talk to you in their language and your own. Bi-lingual intelligent creatures classified as mere animals? Ha! They would take offense. =) But yeah, you need Dragon Call to summon a dragon.