The GTX480 has 352 shaders (approx. GTX460 level) but at only 425MHz core (vs 675 stock for a GTX460), so it ends up with around 2/3rds of the core 'power' as a desktop comparison, closer to a GTS450 than a GTX460.
It also has ~76GB memory bandwidth, between a 450 and a 460.
The HD6870 is 800 shaders at 675MHz giving it slightly more shader power than a desktop 5750. It has half the TDP of the 480 (50w vs 100w) and ~57GB memory bandwidth, less than a 5750.
The 6970 has about 30% more core power (shader * clock) than the 6870 and a TDP of 75w and 115GB/s memory bandwidth.
HD6870 will probably be a little slower, but a lot better when it comes to gaming power use and heat. Don't know about idle, but both of them will clock down a lot under idle and will likely be similar in idle power use.
What screen resolution does the laptop have?