I'm adding an answer because I disagree with the accepted one and I have a different take than jlliagre.
To me they're not interchangeable, and the difference is not in person vs things (you can say "je l'aime pas" for a movie among other things), but unique, specific things vs general things.
Je l'aime pas is for "I don't like this thing in particular":
Ce film, ce candidat, son progamme électoral, cette voiture, ton pote avare, ton gâteau, je les aime pas.
J'aime pas ça is for "I don't like this type of thing":
Les films de SF, les candidats d'extrême droite, les voitures anciennes, les gens avares, les gâteaux aux fruits, j'aime pas ça.
It can get tricky when you're using the plural, and there's just enough things that you could be talking about all of them, but also about them as a kind of things. For example :
Les films de Tim Burton, je les aime pas.
Les films de Tim Burton, j'aime pas ça.
Both work and have roughly the same meaning. In the first sentence you're talking about all the movies as a group of specific things, in the second one you're talking about Burton movies as a type of movies.
It can get trickier:
J'adore Batman, mais les films de Burton j'aime pas ça.
Here you're saying that you don't like any Tim Burton movies, and consequently you don't like the Batman ones, even though you like Batman.
J'adore Batman, mais les films de Burton je les aime pas.
Here, it's implied that you only dislike the Batman movies from Tim Burton, not necessarily all of his filmography (the sentence "... les films Batman de Burton, je les aime pas" is implied).
Note that in some sentences with plural, both forms don't necessarily work:
Les amis de Vincent, je les aime pas.
here you're talking about a set of specific people, it would be weird to use "j'aime pas ça".