I got my Diztronic Gray TPU case today, and since I've been using the HHI (purchased from that $0.99 sale last week) I figured I'd share the differences having them both in hand.
As I said above, I had a Diztronic TPU on a previous phone and enjoyed it although it had a few flaws (excess molding flash around buttons, missing NC mic hole). Being a tightass I jumped on the cheap HHI case deal, figuring I'd take a chance on other manufacturers matching that same quality.
And I was rewarded for my cheapness with a cheap case. The HHI case has two big problems as far as I'm concerned. The cutout for the power button is pill shaped, following the contour of the button and projecting upwards away from the case. It doesn't leave much room for a finger to press, especially when trying to use your index finger when one-handing it. I remedied this with an X-Acto and a soldering iron to smooth the cut, opening up the button hole towards the back of the case. More troubling though is the fit around the front of the case. HHI managed to get the back of the case to fit the curves of the One nicely. However they didn't account for the bevel around the One's bezel. The side effect of this is that the corners don't stretch the front portion enough, leaving the sides to bow out a couple of mm at the center of each side. I don't think this would affect the function of the case in an impact, but at best it ruins the straight line aesthetic of this phone. One lesser annoyance is the molding seam that runs the entire perimeter, which isn't distracting to the touch but is very obvious against the transparent side pieces.
The HHI seems like it would be a functional case from the aspect of being protective: it covers the corners with shock absorbing TPU and protects the bezel where it counts. It goes in and out of pockets easily and the matte clear blends well with the color of the silver phone.
Today the Diztronic came in and the extra $11.51 proved well worth it. The Diztronic case fixes both of the issues I had with the HHI: the power button cutout is nearly flush with the button at the front and back, making it easy to push, and the front fits snug and stays straight along the edges. Like the HHI, the cutouts all line up ok, and while it doesn't make a functional difference the camera cutout is centered maybe 1mm too low. Unlike the HHI, the molding seams are small and in the corners. My previous TPU case experience was with a black case, so time will tell if I'll see this one turn yellow after a few months. If that happens (and supposedly it's inevitable with clear TPU) I'll buy the black version without hesitation.
TL;DR: The HHI and Diztronic TPU cases both do their jobs, but the Diztronic is well worth the extra money for the fit and finish.