Got my second suit today, both printed from the same file. The difference between the regular ZentaiZone fabric and the 'Thicker Shiny' is really subtle. If you didn't know it was there and weren't looking for it you probably wouldn't notice. It feels slightly thicker to the touch, but only really noticeable if you're holding the fabric between two fingers, and isn't visibly thicker. There is a very soft shine to the fabric, I'd not call it actually shiny however. All things being equal I'd get the thicker fabric as it only an extra $20, but I think in reality most people wouldn't notice or care about the difference.
However, the colours on the thicker fabric version I have are deeper and a bit more muted, and seem more accurate to the file (like the TASM1 suit appears on screen, or a bit like DOJ Superman). The standard fabric is brighter (more like the red and blue from Christopher Reeve style of Superman) and the details are maybe a bit sharper, but colour is less accurate to the file. I don't know if this is related to the fabric, or a variation in printing or some other detail.
If I was getting a DOJ Superman I'd ask for the thicker shiny fabric myself, but if the bigger variation is from the printing and not the fabric then it may not matter to most folks. Hope that helps