Cheap Europe flights do not pamper you the way that American flights do. They do not offer meals, free drinks, or even prebooked seats. A lot of times you will have to fly to remote European airports that may be nearly an hour away from your destination. If you are going to do that then you definitely want to make commuting arrangements prior to the flight because some airports do not offer ground transportation. However, in the case that they do, an hour ground-travel is nothing in Europe and your price will still end up being significantly less expensive.
Sometimes you'll find that European flights are more likely to have cancellations than major airlines. They don't provide compensation in the case that your flight is canceled, either. Cheap flights normally don't allow you to bring a lot of luggage on-board either. If you exceed baggage limits they may charge you a very large fee.
The most obvious advantage of cheap Europe flights is the huge discount. You'll generally find cheaper flights on weekdays but even on weekends, prices are lower than flights here! For example, you have a European flight company and an American company, you can find airfare through the European airline for as little as $228! Of course, there are taxes and fees that total about $27. The American airline's fare is $243 with a $54 fee in tax, totaling about $297 total.
There is a reason why rail transportation is much more popular in Europe but these flights are unbelievably cheap. Naturally, traveling by air is going to be quicker than by ground, which gives you the chance to visit more European cities. So, it's all about your own preference when you're deciding to travel through American companies, trains, or to take cheap Europe flights.