Obviously, European airports are like those in the US - inconsistent. On our flight to Barcelona in September, we changed in Amsterdam. We had to go through a security checkpoint and they wanted photo id. I don't know if our driver's licenses would have worked, but we had our passports out and they barely looked at them.
I've heard a lot of horror stories about Heathrow and lost luggage. Our only flights there were ending/starting so there was less handling and we had no problems. Maybe that was because we were on Virgin Atlantic.
I agree with the comment about allowing a lot of time at CDG in Paris. It is not a passenger-friendly airport and when we were there4 years ago, the signs were not plentiful or clear.
Overall, I don't think connections in Europe are any more difficult than in the US. We were concerned about our last connection in Amsterdam with only an hour-and-a-half, but we were at our departure gate about 35-40 minutes before they started boarding (and our flight didn't have a gate, we "tendered in"). And other than KLM posting the wrong baggage carousel in Barcelona, we had no problems there, either.