Looking at the EU policy, there really isn't anything that mandates that your carrier must offer roaming at the same speeds as you'd get in the "home country". Having been a Three customer in the UK in the past (before the rules took effect) and used their "At Home" free roaming abroad, I can say that speeds are usually limited to 3G even when I have a 4G bundle in the UK. So this may be a carrier-dependent thing. The best thing to do is to go into a carrier store or phone them and ask about speeds.

Regarding non-EU vs EU citizens, I would say the only thing that comes to mind is certain packages are unavailable if you don't possess a local national ID or residence permit. Some countries do require certain packages like long term contracts or non-PAYG to be registered to local residents so that would necessarily limit your choice to tourist packages or PAYG bundles. But tbh I doubt that's a huge concern.