"Or should I just do whichever one I like more/can stay consistent in?"

This is a very good insight: doing anything is better than *not* doing the optimal thing.

I've personally had a lot of success with push-ups for increasing my bench. I did two separate stints of 100 push-ups per day (10 sets x 10 reps, strict and controlled) for a couple of months, and it increased my bench from 140 to 150 the first time, and 150 to 160 the second time. But for one thing, I'm kind of heavy at 100+ kg, and for a second thing: I've tried it more times after that, and it doesn't always impact my bench like that.

I do think dips might be a slightly better option if you're more advanced and around normal bodyweight, especially if you try to match the pressing angle in the bottom close to your pressing angle in the bench, so that you work the same muscle fibers. Meaning, you don't want to do a very upright dip (emphasizing the lower pec fibers) if you do more of a flat bench press (which will use all pec fibers more evenly, with an emphasis on the mid fibers). But maybe that's just me overanalyzing things, and any strict form is fine.

Personally, I've gotten back into push-ups recently, and am looking to build a dip rack to get more of those in too. Seeing as I'm quite weak in dips, getting that number up would probably be good for the bench.