I think "trump" has something that "surpass" doesn't.
If A trumps B, there is no element of a comparison of strength. No matter how strong B is, A wins.
An example of a situation where love for animals trumps concern for other humans ... ...
There is a huge multi-vehicle pile-up. Damaged vehicles are strewn across the highway.
You arrive on the scene, and the first casualty you deal with is the hungry kitten mewing on top of the mangled car.
To panjandrum. The sentence was used in the context below. So I think the example of a situation you mentioned applies here.
"You have come across a burning building. From inside,you hear the howls of your beloved dog and the screams of a man you don't know. Flames licking at your heels, you run into the building and realize that you only have time to save one or the other. Which one should you choose, the dog or the man? "