The only gripe I have with them is they are naturally heavy as lead on the forehand. You feel like you're riding a wheelbarrow - downhill all the time. And jumping . . . forget it! They're not jumping horses.
They also are not very speedy. I went to see LOTR with a friend, and we noticed in the chase scene with Arwen and Frodo running from the Black Riders that the Andalusian was going full tilt, while the Black Riders (on their T'breds) were having to hold their horses back to avoid overtaking the Andalusian.
That said, I think the Andalusians have the most noble heads and necks of ANY breed on the planet.