For me it is a few things, a lot mentioned by previous posters. Some of it is DF specific, others just fantasy in general.
In game the biggest for me is the FPS they steal when they bring their useless caravans. In general it is the way they're usually portrayed in fantasy. They're perfectly beautiful, aloof, good, magic, immortal, and living peacefully in nature. The problem is they're too "perfect", they don't have any serious flaws, and so they're bland and boring. Even the flaw of them being aloof isn't usually expressed as a flaw.
Now dwarves have several flaws. And it is as much, if not more so, the flaws that make a great and interesting subject rather than just some perfect creature. Dwarves are stubborn, but out of this comes the focus to create great works. On the one hand they're rowdy drunks, but on the other they can focus this wild energy in battle to destroy their enemies with rage. At times they can be crude, but they are also unwaveringly loyal.
So the cat vs dog comparison is apt in this situation. Dwarves being the dogs and elves being cats. Dogs are obedient, loyal, can do jobs and tricks. Cats lay around being smug yet ultimately useless and their owners have to clean up their shit (who is the pet here?).
Now, if elves were tweaked a little, they could be more interesting. One way to go would be the drow or dark elf route. A deeply hierarchical society thick with social maneuvering, intrigue, betrayal and assassination. A highly structured surface that is evil at the core.
Or the wild elf way, where elves are savage xenophobic creatures who stalk the forests looking to kill any intruders and living decadent lives full of hedonistic parties around the night fires while consuming massive amounts of feywine. Feral on the surface and completely alien underneath. Not evil, just utterly foreign to the ways of dwarf and man.