Basically the main difference is that most P55 boards have x8/x8 crossfire whereas H55 has x16/x4. The x4 will bottleneck a HD5770 so if your looking to crossfire you should look towards P55. Though if you aren't or you think you might have a small chance of CFing then get the H55.
Also most P55 board have a few more features. Like onboard RAID. Also if your into high end OCing the P55 would be best. Though a H55 would be good enough for any 24/7 air cooled OC.