Just curious, but why can't you just bring your Model S with you?
Is it something technically specific about the Model S (e.g. charging)?
Or is it something general, like a prohibitively expensive import tax?
Or what?
In fact, what is a US Model S vs a "European one"?
There are some subtle differences in things like airbags I think, but the big difference is charging, driven by the difference in the power grid and possibly EU regulations.
In the US, three phase power in only present in industrial areas - homes have 240V power, but only a single phase of it.
As a result, EVs built for the US aren't designed to handle three phase power. When Tesla originally developed the Model S, they decided the new SAE standard charging outlet for EVs didn't suit their purposes, so they built their own (and provide an adapter to it with all U.S. cars for public charging.)
Obviously this custom single phase outlet wasn't going to work well in Europe, where three phase power is much more common. Also, EU has mandates about commonality of charging I think - certainly that's why every cell phone for the last decade has used micro USB to charge (except for iPhones, of course - and they ship and adapter to micro USB with every phone in the EU.)
So for Europe, Tesla developed a charger that can handle three phases, and adopted the Type 2 standard there for the car and the supercharger.
Thus, a European Model S can't use a U.S. Supercharger, and vice versa. A U.S. car in Europe can't charge quickly most places (no way to get three phases into the car, and the charger couldn't use them anyway,) and a European car in the U.S. may not be able to, either (not 100% certain, but I don't believe the EU charger can use 80 amps delivered on a single phase.)
The signaling is the same in both regions, though. In principle Tesla could deliver an adaptor for Supercharging, if they can deal with that much power in it, and either car can charge in the other region at reduced rates.
Edit: Apparently I wrote too much. I carefully checked that you didn't have an answer before I started writing, and GSP beat me to it anyway.