|Charlie Brooks RPG Superstar Season 9 Top 4, RPG Superstar 2015 Top 32
Speak with Animals looks to be a lesser version of the feat.
Both give you:
You can ask questions of, receive answers from, and use the Diplomacy skill with animals.
But Speak with Animals continues to say:
The spell doesn't make them more friendly than normal. Cunning animals are likely to be terse and evasive, while less intelligent ones often make inane comments.
and Animal Empathy only says:
In most cases, wild animals will give you time to make your case.
So in good circumstances, the two will have the same effect - being able to use diplomacy and make requests of a friendly animal. But in a less good case, Animal Empathy will let you do it to an unfriendly animal.