Which do you prefer, going to a movie or going shopping?
Which do you like better, going shopping or going to the movies?
例えば、映画を見るかショッピングに行くかを聞くなら次のように言えます。
ーWhich do you prefer, going to a movie or going shopping?
「映画に行くかショッピングに行くかどっちがいい?」
ーWhich do you like better, going shopping or going to the movies?
「買い物に行くか映画に行くかどっちがいい?」
to go shopping で「買い物に行く」
to go to a movie/the movies で「映画に行く」
ご参考まで!