Wow, what a sensitive subject. It's a difficult answer, especially since I am neither black nor gay. But I will give this a go.
First of all, I think most people relate "Civil Rights Movement" with the plight of the African-American Community here in the states during the sixties. But let's look at the definition (according to Merriam) Civil Rights: the nonpolitical rights of a citizen; especially: the rights of personal liberty guaranteed to United States citizens by the 13th and 14th amendments to the Constitution and by acts of Congress
Since slavery does not apply here, let's look at the 14th amendment,
1. All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside. No State shall make or enforce any law, which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.
Ok, sounds like the gays qualify.
Now how about, how similar is the Gay right movement & the African-American rights movement?
1. "Who had it worse" arguments never work. The biggest difference here is that the African American civil rights movement began with slavery. A crime that was allowed by our government, which set a VERY VERY long and arduous path for the African-Americans to walk. That path they paved is why the march of the gays is not going to be quite so arduous. Which is why the black community and gay community should really be embracing each other. And if the gays really want to change things, they need to look at the black community to see how it's done.
2. At this time because of the animosity towards gays, we have no real idea how many gay hate crimes occur everyday. So it's hard to say what the casualties really are. Same with how many gays are treated badly in such a passive way that it can't really be proven that it was related to them being gay. Except for the massacre of gays during the holocaust in Germany. Such animosity towards gays is why this moment in WWII history is not even taught in schools. Read the linked article, and then tell me that the gays have not suffered. They have.
So yes, it is similar on the sense that every civil rights movement has the same goal, which is reinforcing their civil rights as guaranteed by the 14th amendment?
And it's different for two reasons.
First of all, every movement has it's own unique story to tell. African-Americans, Gays and yes, women's suffrage even. Heck, even the Irish Catholics couldn’t' find jobs when they were fresh off the boat. They could barley eat in restaurants outside their own neighborhoods. Until Joe Kennedy came along and had a son...but I digress.
Second, the gay community is unique in the sense that there are many many black gay men and women. Where is their voice in all this? How can we ignore the fact that here is a community that includes people from EVERY other oppressed group in history? That must mean something.