Which is a better UA strategy: Multiple campaigns with small budgets or very few campaigns with high budgets?

I'd say it's rather tactics than strategy, and not so much about budget (if you're reaching your daily budget, you're likely to be losing performance, opportunity or both) than it is about account structure.

My personal (hence biased) experience is that it used to be best to have many adsets running, with placement/language/audiences/... splitted and managed separately. Definitely less the case since February 2018, not what reps would recommend, not the best for management time effiency, but especially: not if you moved to AEO & VO, with which fewer campaigns/adsets with larger audience often makes more sense these days.
It's not all black & white though, I've seen success having a bunch of narrow adsets (ex: LAL1%, specific placement...) work well in parallel of a huge adsets on AEO/VO and large audiences/placements selection. Best of both worlds?