Media thickness is still the same for the Z printers being 0.8mm about half the max thickness of Epson. With both you can exceed their max capacity but marks on either side and or head strikes.
Cut sheet loading is and has always been easier on Epson. The new auto clamp roll system on the Epson is also a leader in this respect. Personally I don't have any problems loading the 3200 but could only find the Epson 9900 that much easier.
B+W on both should be very similar in every way. On certain photo media the HP with Gloss Enhancer all but eliminates gloss differential, and on colour it is just slightly ahead of the competition. I use it on eco mode where it only puts GE on the areas needed namely lGrey, lM, lC, and combinations thereof. Epson changed the color maps of the grey inks and GCR used according to users. I assume it is closer to Canon and HP now with high GCR. If so (and from the print samples I have seen) the B+W is going to be close.
The advantage of HP is you can batch print colour and B&W side by side on the same print job with no composite colour in the greyscales as the driver only uses grey inks in equal value rgb. So when the values are say 40 40 40 in that area only grey inks are used. This leads to a more neutral less problematic grey for varying view lights. Gloss Enhancer is very good but do know it is fragile.
I did a lot of testing on the 3100 and by doing so saw the changes , too many to count. This is simply no longer true of the 3200. It is stable and just works. There were vast improvements made to the included HP profiling, and even more with the APS. Apparently marketing decided to stress the fact the reds were effectively improved ( yet it was a problem on reds on certain media before) but the other improvements didn't show the real reasons why it is a a large step up in the right direction over the old 3100.
I also tested for ImagePrint over the years. I've finally settled on using Qimage on both a MacBook Pro under boot camp or a real PC for any production printing. Being it is just a front end , it only uses the driver without a separate application. I will never use a rip again , and happy to not have to.