no difference in speed in regards to pcie version. both pcie2 and pcie3 have enough bandwidth for even the fastest gpu's out. What could be a problem is the power supply you have is only 250w. It may not be enough for that gpu. You will also want to make sure there is an exhaust fan to remove the extra hot air that builds up in your case.
"Here is Guru3D's power supply recommendation:
•Radeon HD 7770 - On your average system the card requires you to have a 450 Watt power supply unit. "
you should be able to get away with a good quality 380w unit to like the antec earthwatts 380w. the 7750 uses about half as much power, you may be able to get away with it, but HP's 250w PSU's normally have pretty poot output especially on the 12v rail.