Dareen,
There is no catch, and yes, it is usually cheaper to do a rating in the USA than in Europe. The biggest cost advantage for going to the USA is often on the hotel and living expenses; the biggest disadvatange is the extra travelling time. Add to that a competitive exchange rate, and I have almost always ended up going to the USA for my ratings and renewals.
As Flugzeug says, they are the same type rating, and apart from a handful of differences the CJ1 and the CJ2 are exactly the same to fly. (Obviously all the magic numbers of power settings, speeds and so on are different, but if you are just starting out you'll not have memorised them yet anyway, and they are in the same place in the book whichever model you are sitting in!).
If you have only flown the CJ1, a couple of hours with the books would get you into a CJ2.
Beware however that the "plus" versions (CJ1+, CJ2+ and confusingly, CJ3) all have different avionics and FMS setups to the non-plus (CJ1 and CJ2) versions. It is very unlikely that you would just "jump in and go" in one of those, unless you have prior experience with the Collins FMS operating logic - you would probably need an avionics differences course (I did).