Which verb form should I use with word "Prefer" related to the following sentences?

Question

They prefer to go (or going) for a walk to watch/watching The game.

My question is should I use 'watch' or 'watching'

Answer 1

Taking your precise question, I would choose:

"They prefer going for a walk to watching the game"

Though this rather implies an ongoing general preference relating to some generic walk vs some generic sporting event important enough to be "The Game" rather than "a game".

To address a more common case of prefernce re a specific sporting event there is an element of consideration of the future :

"They would prefer to go for a walk than to watch the game"

or reflection on the past:

"They would have preferred to go for a walk than to watch the game"

I would though struggle to define the precise gramatical rules that makes this so, and there are lots of variations on the sentence making different comparisons between the two.

Perhaps someone can pin down a precise reason - or argue otherwise.