For the past eight series, their has been no public vote and all the evicting has been done by the housemates.
In BB1USA, they used the format we all know - where the housemates nominate and the public evict, but it didn't go down well that well so they changed it.
They never have a crowd I think for a few reasons, the biggest one being that evicted housemates usually enter the "Jury". The Jury are made up of the last seven evictees and it will be up to these seven to decide who will win. If their was a crowd I think there could be a risk of a member of the public telling a evicted housemate something they shouldn't know. However, there is a small crowd at the finale.
Also, BB4USA was broadcast on E4 in 2003, after BB4UK
The closest thing they have had to a public vote in recent years in is BB8US, when one housemate (Eric) was called "America's Player". America could vote online for free for who they wanted Eric to vote to evict, who they wanted him to try and get nominated and more.