I like 1 and 2 a lot, especially 1.
On #1 the background has a lovely color tone and the blur is very nice and the bird pops. The BG tone is relatively even except for the dark spot to the right and below the bird. It's not enough to combat the bird, though, so the image works well.
On #2 it's not so even - the upper left corner has dark and bright tones which distract from the bird. But then there's a realization that the bird is flying to this spot, and the image makes sense. There's almost combat, but instead there's a flow. If the bird was flying at any other angle it might not work so well. And the background directly behing the bird has nice tone and blur again, allowing some nice pop.
The last one has little/none of this and doesn't work for me. I think it has more to do with the background contents - the dark center distracts, and the bird has a balancing bright spot on the other side of the dark center. This confuses my eyes - which bright spot do I look at? And the rock that the bird is on is in focus, so doesn't have the pop of the first two.
Does that make sense?
All in all, by all means take the shots with a background like this! It's more difficult, since you seem to be above the bird so the lighting is more difficult. But when it works, like #1, it really shines.