What are the similarities and differences between a sweet16 and a quinceanera?

Well, to start off, a "sweet 16" is celebrated on a girl's 16th birthday.

The word "quince" means "fifteen," in Spanish.
So, a quinceañera is actually celebrated on a girl's 15th birthday, and not her 16th.
Latin-American countries are the ones that celebrate la quinceañera. Obviously because they're the Spanish-speaking countries.
On the other hand, the Sweet Sixteen is celebrated mainly in the United States, and in Canada.
But those two events, the Sweet Sixteen, and la Quinceañera, revolve around the same purpose.

They are both meant to celebrate a girl's transition, from girlhood into womanhood.

What that means is that on a girl's 16th birthday (in America) or on a girl's 15th birthday (in Spanish speaking countries) it is the first day in her life, that the girl is considered a woman.