I think the difference is probably rule-based. Some US military pilots were disciplined some time ago for busting minimums on a sports stadium flyover that looked pretty modest. I think the brass hats keep the demo teams on a fairly short leash.
I've seen the Blue Angels and Thunderbirds any number of times and also single ship demos of F-15 and F-14 (back in the day) and A-10, maybe some others I don't remember. Of all of them, the F-14 put on the best show but, a) it was about 1982, I think, so different rules, and b) it was a clear, cloudless day with no ceiling. Most of the other demos I've seen had some level of ceiling or at least scattered clouds that probably constrained what they could do somewhat.
My perceptions of...
- Loudest air show event - Blue Angels C-130 Fat Albert doing a JATO/RATO takeoff.
- Loudest air show take-off/flyover - B1 Lancer, going at the speed of heat (Six Blue Angels FA-18s a close second - twice as many engines as the Thunderbirds doing the same thing in F-16s)
- Loudest sustained airshow event - Harrier in hover
If you really pay attention, the pre-main event for the Blue Angels is a demo of Fat Albert by her USMC crew and they REALLY horse that thing around, including steep bank turns at about 1-1/2 wingspans from terra firma, short field landings and takeoffs, backing up on the ground, etc. It's just a warm-up for the FA-18s but they put on a pretty good show. Of course, they're probably very lightly loaded when they do that, but still pretty impressive.
Haven't seen any demos by non-US military pilots except the Canadian Snowbirds, a long time ago. Very precise and artistic, as I recall, but the aircraft they fly are not in the same performance category with 3rd and 4th generation fighter types.
An observation about the big name demo teams and something probably overlooked by most - in a typical show they do a number of routines that end up with four (or sometimes six) aircraft heading off in different directions at high speed, sometimes at different altitudes and attitudes. Despite that, in 45 seconds, they're all back together, at the same speed and altitude, pointed in the same direction, positioned for the run-in to the field for the next maneuver. That's a hell of a lot more difficult than most people realize and speaks to hours and hours of planning and practice. All the teams I've seen seem do it equally well.