Yes I do think they like certain music like we do. The beat, the base the instruments??? I don't know why they like certain pieces more than others. I just invested in a talking and singing parrot toy, not cheap at �60 but it is remote controlled can say what ever you want it to say in a parrot voice, dance and sing to its own song, or dance to your own music. I bought it just to wind my cockatiel up called Nile's. As Niles is extremely nosey and noisey, and over reacts to everything, so I have called the parrot 'Joey' and put him next to Nile's cage and he goes nuts I know he likes it because he tries to get closest to the parrot as possible. I also make the parrot say rude and crude things which is very funny. I plan on filming Niles and Joey and putting it on youtube soon if I do I will paste a link sometime in the future for you to see.
My guinea pigs and rabbit also seem to lisen intensely to some music, usually more instrumental jazzy stuff, like Sting, phil collins, eric clapton.