Yep. And at least in Western Europe the LTE bands are all the same, so if it works in one country and not another, it's not your phone.

I have the same issues with my work phone's Belgian subscription SIM--it works great in the Netherlands and France, but is a serious pain in the UK. In the US it was nearly useless because T-Mobile barred it from LTE so the iPhone would always grab T-Mobile and then get kicked to EDGE for no apparent reason.

If your home carrier recommends a particular roaming partner, you can lock your phone to that carrier when you cross the border. That was the only way my phone was usable in London and DC.

Also worth noting is that although the EU forbids carriers from charging for roaming, it doesn't require them to provide LTE access. I can't speak for your Austrian carrier, but Three UK has provided HSPA only outside the UK as part of "Roam Like at Home" for a couple years and continues to do so now. In theory they could limit roaming to EDGE, but the argument that they're not actually providing roaming at that point would probably be a valid one.