After measuring, it seems that both parts should fit, though in my research I've heard some people mention that they had issues upgrading the psu on the i3 version of the h430, (such as needing to update their BIOS). I figured I should ask here in case I happen to be looking into hardware that may cause problems, as I am not very tech-savvy.
Since I originally bought this as a budget computer, I don't plan on adding any upgrades other than the ones mentioned here.
As long as the dimensions and form factor of the power supply match you should be good to go. BIOS update shouldn't figure into switching a power supply. They were probably talking about the video card compatibility.
Case looks like a small mid tower, so your 7850 should fit fine.