I'd venture to suggest that they do matter, but they're only part of the question.
I'd be very suprised if, assessed in that role alone, a 15000 hr airline pilot wasn't a lot better in most cases than a 3000 hr airline pilot.
Similarly, a 600hr PPL is likely to be far more experienced than a 200 hr PPL. But as you say, flying different aeroplanes, out of little strips, has a lot more to do with it. The landings idea is a good one.
If you talk to test pilots, they don't talk about hours much, but about types - a really experienced TP might have over 150 types, but still only a few thousand hours.
In all these cases, the more hours you've got, the more opportunities you've been exposed to for things to go wrong, and you've presumably dealt with them (more or less) successfully.
Current regs consider currency in terms of hours in the last 2 years, and take-offs and landings in the last 90 days - so these rules don't just consider hours either.
G