more features (CUDA/Physx)
Better (subjective) driver support
Better tesselation performance
High power usage
High heat output
No support for 3 monitors without SLI
Lower heat output
Lower power usage
Native 3 monitor support (6 monitors with 5870 Eyefinity 6 model)
Additional monitors with each card in Crossfire.
Support for ATI stream
Worse (subjective) driver support
Both cards have:
Direct X 11
Onboard HD video decoder (supported in ATI's Cat 10.6 driver)
That's a basic list. Remember that the GTX 480 uses A LOT more power than the HD 5870 but only produces 10-15% more performance overall.
I chose the 5870, and I haven't been disappointed yet. If you want to use 3 or more monitors, the 5870 is a no-brainer. If you only use 1 or 2 monitors, take your pick. You really can't go wrong with either of them.