Please elaborate. I would love to know whether you mean that they have (a) more rights than others, (b) less rights than others, (c) different rights than others, or (d) individually different rights among themselves.
It's a little more complicated than that, and varies by jurisdiction, but generally, it comes down to whether or not you understand your actions.
Someone with a learning disability - or Down Syndrome, or mental health issues of almost any kind - can often sue to void contracts that they've signed; or their guardian can sue on their behalf.
People with mental illnesses and disabilies like down syndrome may not have legal capacity if illness / disability affects their judgement sufficiently. Which means they can't enter into contracts by themselves and don't have complete freedom over decisions in their life.
