i have just the answer for you.

i used to be a powerlifter. i switched to olympic lifting. i compete in regional comps and do ok. that's just to give you a sense that i lift somewhat "seriouslY".

anyway, in powerlifting, you alternate grip your deadlifts, which doesn't transfer to oly lifting at all. so my deadlift/cleans really plateaued because my double overhand pull grip was so weak from alt gripping. i could alt grip DL 550 lbs, but i struggle double overhand 405. (used to)

i got stuck here for a while, i tried everything: farmer's walks, deadlift holds, plate holds, those hand grip squeeze things, etc. they worked, but it was SLOOOOW.

so i decided to climb. like... climb 3-4x a week. after 3 months of climbing, i was able to match my alt grip deadlift with double overhand. i.e. my grip strength exploded and allowed me to grip things i couldn't grip before.

TL;DR: most casual lifters don't train grip. in fact, most powerlifters don't train grip either -- they kinda sorta cheat with alt grip. and most oly lifters kinda cheat too, with hook grip. (these grips allow you to hold more weight). can't cheat in climbing though. i would say that if you matched up a similar sized climber to a similarly sized lifter, the climber would win out (some sort of grip competition only, not deadlifts or anything)