Well, overall I suspect a ceramic (or Pyrex) dripper's main differentiating characteristic from the copper one would be that the former material has a higher specific heat. So if you don't preheat it properly you may find the beginning of your cup brewed under temperature. Although I don't think this is a major worry, as you should be pre-heating your vessel and presoaking your filter which also serves to preheat the dripper.
Aesthetically, the copper one is quite a bit more handsome.
I don't use the Hario drippers for a vessel; I use them when I wish to prepare mugs - usually, one , or two - occasionally, three - mugs of coffee (otherwise, I will use the French press).
But, I always preheat the (le Creuset) mugs, and the drippers, before making the coffee.
My copper dripper is Japanese, - and a slightly different shape - rather than an actual Hario dripper, and takes different filters. Thus, the process of pouring - and preparing - the coffee tends to take a little longer when using it.
However, I use copper quite a bit - and not just for coffee. I have a set of Le Mauviel pots, pans, and casseroles, - copper lined with stainless steel - and they cook superbly. Personally, I'm a huge fan of copper, and I love the ceramic Hario dripper - it is painless to use, - but, as
@mobilehaathi suggests you do need to preheat it (and preheat the vessel and/or mugs).
[doublepost=1490396465][/doublepost]And,
@Dave Meadows - the other thing about Hario drippers - it is the fastest way of preparing an idiot-proof (but tasty) cup of coffee. The French Press (especially when I am grinding the beans by hand) takes a lot longer - heating the FP, the mugs, grinding coffee, then letting it steep - etc.
I will rarely have a pot of French Press coffee prepared in under 20 minutes, which is why it tends to be reserved for pottering about at week-ends, or when I have 1) guests & 2) lots of time.
On the other hand, the Hario dripper is far faster, and - I have found if I have one guest, and need to make a good coffee - fast - the Hario method is what I will use. Two mugs, two drippers (that was one of the reasons that I bought a few); sometimes, in my kitchen, you may even lay eyes on three mugs - with a dripper perched on top of each one of them, busily preparing coffee.