VFR at night isn't allowed in mainland Europe, but in the U.K., an extra period of training leading to a night rating is required to enable a PPL to fly VFR at night. Until now, the big difference between U.S. and European private aviation has been the cost. Flying in Europe is much more expensive, on the face of it. User fees there contribute a large proportion of the expense. Landing fees are especially a problem.
Twins are prohibitively expensive.
The rest of the continent is about the same. The biggest factor is gas. Another significant factor is utilization. In the U.K., in particular, the weather is generally very poor compared to, say, Florida or California. If you're an FBO renting out an aircraft in Florida, the weather is so good that your annual running costs for a particular plane are covered by perhaps mid-March, because utilization is so good.