Edwin Battistella's Bad Language p. 98 (2005) explains the supposed superiority of "disabled" over "handicapped":
[O]ne can argue that disabled is the optimal choice on the basis of conciseness, accuracy, politeness, and connotation.... The term handicapped ... carries the connotation of being held back in some competitive enterprise (we talk of social handicaps, golf handicaps, and racing handicaps) and is unwelcome by some people with disabilities.
I've heard this argument from others as well.
But wait: The term disabled carries the connotation of not being able, which surely holds one back in various enterprises, competitive and otherwise. In fact, if you're looking at the connotations that stem from the word's visible etymology, "handicapped" seems more favorable — it suggests that someone's path is harder because of the burden under which he labors, but it does not suggest that he's not able. Horses or golfers who labor under heavy handicaps may sometimes win. Horses or golfers who are disabled (in the literal sense) don't win.
Now etymology, even visible etymology, will only carry you so far; there are other aspects to this issue, which I've touched on elsewhere (here and here). But if one does focus on visible etymology, it seems to me that "handicapped" should be the superior term.
Related Posts (on one page):