Theoretically, you could have a phone that offered both technologies, but I have not heard of one. Previously, you wouldn't have been saving much money, but with the new expensive touchscreens, it might happen. It would be a little confusing, since a GSM phone can be unlocked and made portable, by switching SIM cards (the provider can lock it without your knowing it, and they often enforce their contracts that way). A CDMA phone is essentially tied to the provider - it is possible to switch them over, but it doesn't happen as much as it happens with GSM.
Europe is almost entirely GSM. As long is the phone isn't locked, you can switch phone companies by switching SIM cards. I wouldn't be surprised if in Europe it is illegal for the companies to lock your phone, so any phone would work for any company.
I like the European system much better. Back in the 60s and 70s, Europe was dominated by big companies with government connections - often owned by the governments, and they would have had things like locked phones, while we would have had a more open system (though not with old Ma Bell, the exception). Now the companies here are so influential in government we have a closer connection between companies and government than the Socialists of the 70s could have dreamed of.