different games, different pipelines. the 7770 is prolly the one that will give the best compatibility with your configuration. but it requires an additional 6 pin power plugin off of the power supply. the r7 250 does not. i will look into your hp further for the crossfire capability, if it does offer crossfire with your apu, i would go with the r7 250.
ok, crossfire is capable, with a specific uefi bios tweak procedure (legacy boot, turn off safe boot, then turn on integrated graphics. all that in separate boots. so, the r7-250 is compatible in crossfire with your setup. if the discreet option is standalone, then the 7770 is the way to go.
either way, i always have liked the asus radeon cards, and be sure to get the gddr5.
Edited by synergy513, 23 December 2013 - 02:03 PM.