For starters, in Europe, a lot of the cars are shared, meaning basically as you cross into different countries, the cars are the same. It's like our country in relation to Canada; our cars are pretty much the same as the cars that are in Canada.
In Europe, there are many more brands than what we have here in the U.S. Here are just some of the most popular "normal" ones (meaning, not any super sporty types):
Renault - French company
Citroen - French company
Peugeot - French company
Alfa Romeo - U.K. company
Fiat - Italian company
Like I said, there are others, but these are among the top car makers there for normal cars.
Of those companies, probably you have only heard of Fiat, or possibly Citroen. Last year, Fiat bought a large portion of the Chrysler company, in an effort to keep the company from going under. We have yet to see any Fiat branded cars here in the U.S., but they could come sooner or later. Citroen had a short period of time here in the U.S. It was quite a few years ago (between the 1950's and 1970's) so chances are you've never heard of them (I hadn't either).
The first couple of days during my trip, all of the cars were a blur to me. That must be what it's like for the people that do not know their cars or quite frankly don't care (which I'm sure there are many people like that and I understand, don't worry).

As the days wore on, I began to pick out a couple that I kept constantly seeing. There was this one car called the Renault Kangoo. I remembered it for a couple of reasons. The primary one is because of the name- who wouldn't like a name like Kangoo? Not only does it sound like "Kangaroo," but it has a zing to it. This French car company has some very good marketing people. The second reason was because one of these vehicles nearly hit me as I attempted to cross a busy street. At this point in time I also was able to hear the horn. The horn sounded strikingly similar to a chihuahua barking at a mail man.
Anyways, that was one of the main cars that stuck in my head, and for good reason too.
The other car that I remember vividly from the trip was the Renault Trafic. It was, again, a neat name.
Another reason for the overall compact feeling of their cars is the fact that so many streets are narrow. Our huge touring bus had to creatively navigate the small streets in many small cities and towns, not to mention the metropolis of Paris. There were many nasty words uttered in Romanian by our bus driver, whom was from Romania.
If they had all the huge SUVs and cars we have here, I don't think they would be able to cope. You would see a lot of missing side-view mirrors, missing bumpers, and scraped doors because of the difficult navigation that needs to happen. Additionally, a lot of drivers there are crazy.
When it comes to liking which area's cars better, I would have to say I like ours. This is obviously because I know way more about them and that I've been around them my whole life. The cars abroad were very different and unique and I think a few should come over the pond and be sold here in the U.S. I think some of the cars would do very well over here.