It depends on the event and the event holders.

"Ren Fairs" in the US are more likely to be put on for fun. Go hear a guy in tights play a lute, eat a roast turkey leg, etc. I think convention cosplay culture is starting to leak in.

If you want to see Americans take period costume seriously, go to a "reenactment." You'll find folks who are very serious about history, many of them are professional historians, archaeologists or museum employees performing for the education of the public. Probably the biggest community is the one around the American Civil War. Go watch the movie Gettysburg. Sure there's the main cast of Hollywood actors, but then there's hundreds and hundreds of extras. They're war reenactors, who showed up with their own personal uniforms and equipment.