Historically, Roma people were slaves in Moldavia and Valachia (principalities of today Romania) up until the middle of the 19th centuries. Unfortunately, there is no discussion about their slavery or the consequences of their slavery. Without any discussion of this historical fact, it is very difficult to understand the structural oppression Roma peole has suffered.
Yes, the European Roma struggles are much like the African American rights struggles. Both were/are a class of people who are looked down upon and stereotyped because of the way they look and because of preconceptions that people have about them. Both were and are often not given the same opportunities as other members of society.
European Roma struggles mirror the African American civil rights struggle in some ways, such as this being a people of certain look and background that sets them up for discrimination and hate. In other ways, though, it is true that there is a Roma lifestyle that many people would be wary of.
The Roma people, or gypsies, are discriminated against in Europe because of their traditional, non-modern ways of doing things. The nomadic people are struggling to survive in modern Europe because their beliefs often clash with contemporary norms. Mainstream Europeans simply don't understand the Roma ways and fear them, which leads to discrimination, much in the same way African Americans were discriminated against for 200 years.
It does not seem as if the Roma were brought to the European countries involuntarily. Instead, thy roam of their own free will. Yes, there is some discrimination based on the darker looks of many, but they were never enslaved and they do have a culture that is totally their own and they like it that way.
The European Roma struggles are not anywhere similar to the African American rights struggle. The primary reason for this is that the Romani ("Roma" is kinda racist, by the way) have always insisted on being as physically and culturally seperate as possible from the rest of Europe. Most of the barriers are their own making.