Accurately portraying someone with physical or mental issues is harder IMO. It's hard to make it look "real" compared to playing another role because there are more of the "little things" that you have to get right or it looks like you are acting rather than a brilliant actor who makes it look real. There are so many nuances and subtleties involved. It's easy to overdo or "underdo" it I think.
For an example look at Hoffman in Rain Man. Watch his eyes and his arms and his head movement. Those little things carried the role IMO and I think he even won an Oscar.
