Leatherface – the original Leatherface, not the more farcical one in TCM 2 where he pseudo-humps Stretch with his chainsaw in beat-you-over-the-head-phallic-symbol way, although I do love that one too – is sympathetic in a way the others aren't. The terror of Michael Myers is his blankness; his generic Halloween mask emphasizes how little is going on behind there besides just the desire to kill. And Freddy – well, the dude was a child molester. Enough said.
But Leatherface, while he does bludgeon the free-wheelin' teens who find their way into his house of horrors, is sort of kerfuffled by the whole thing. In one scene, he mutters to himself, shaking his head by the audacity of the kids who are interrupting his normal day-to-day life. His home life is pretty messed up; his brothers pick on him, his grandmother is a dried-up corpse in the attic, and his grandfather is barely able to feed himself. And as far as the killing, he doesn't seem to see the people as much more than two-legged cows; he bludgeons them, hangs them on hooks, and stuffs them in freezers. He's just doing his job, as far as he's concerned.
One of the most interesting scenes is the dinner scene, the climax, where Leatherface is wearing the traditional "good housewife" apron and a face that's painted with makeup. These were both things that would be looked down upon the second wave feminists of that time that were rejecting the housewife role (although it's debatable whether they would have been watching at all) and would be seen as emasculating by both the male horror viewer as well as by his family. (It's also a nod to serial killer Ed Gein, who very loosely inspired TCM and was infamous for dressing up in the skins of his female victims, among other things.) So even though he's the one with the chainsaw, he's still the whipping boy of the family.
In the remakes, Leatherface is two-dimensional. There are a lot of subplots about inbreeding and close-ups of his torturing his victims and not much else. He's a monster in the original, yes, but he's behind the mask somewhere in there.
Also, the man does an impromptu chainsaw dance at the end of the movie, with a pirouette and everything. Check it: