Both use the same pickups and the preamps in each have the same boost/cut at the same frequencies. Only real difference is the USA used a Korean built PCB and the BXP had a SMT module.
Alder bodies with a decorative cap was standard for both BXP & US as was pau fero boards. Most BXP did come through body with single saddle bridges but then Peavey thought that was good enough for the US "custom" bolt-on versions.Those bolt-ons used the surplus preamps from the,then, recently discontinued Millennium. Always smile when I hear folks brand those Millie preamps as an upgrade,it was simple economics 😄
Must say I'm surprised you think there's such a huge difference between the BXP version and the US. Last year a friend picked up a BXP 5'er on her travel up to visit,lovely darkwood model it is. With Gill's 3 US and my 4 it's safe to say we know the Cirrus tone well. Her latest looked,played and most importantly sounded exactly like a Cirrus.