(In alphabetical order)
1) Air Supply
Although they were already big in their homeland (Australia), they were even bigger in America. Particularly they had 4 Top 10 hits in Australia, and in America 8 Top 10 hits. In fact in America they weren't only Top 10, but Top 5. In Australia they had only one Top 5 hit, particularly their first single Love And Other Bruises .
2) Black Box
It's not common for a House Group to do well in America, but Black Box did. They had 3 #1 hits in US Dance Chart, and 2 Top 10 Hits in Hot 100 Charts. In their homeland (Italy) they were clearly less successful. Although they did better in other European countries.
3) Cutting Crew
Sure they had success in their homeland, but they were even bigger in America. Except Died In Your Arms, popular singles (by then) I've Been In Love Before & One For The Mockingbird. Also later they had 2 Top 20 hits in US Adult Contemporary charts, with singles Everythign But My Pride & The Last Thing.
Both didn't chart in British charts.
4) Def Leppard
Although when they started they did better in UK, but since Pyromania they became extremely popular in America. Particularly their albums Pyromania and Hysteria , reached Diamond status. Although Hysteria reached #1 in the UK as well, it wasn't as popular as it was in America
5) The Fixx
I don't know how it happened, and The Fixx have been so largely ignored by British audience, but they are definitely one of the Top bands about being ignored in their homeland. Fortunately for them American audience gave them the chance they deserved, and this magnificent band didn't get "lost".
6) Kingdom Come
Although their debut album, reached Platinum status in Germany (their homeland), no singles made it in German charts. They had 5 Top 40 hits in US Modern Rock Charts though, and their single Get It On reached #4 as well. Seems like Hard Rock is a pretty successful genre in America
Their single Your Love has reached #1 in US Dance charts. And so many other singles as well made it in Top 20 in Dance Charts. Definitely a highly successful Hi-NRG band in America.They did better than they did in Canada, their homeland. They had other 2 Top 10 Dance Hits. Have a look here.
In Canada only Your Love reached #1 according to my research.
Listening to them, I'd swear they are Americans. They don't sound British at all. But surprisingly enough they are British. No surprise why they lacked success in their homeland though. Their song Voices Of Babylon was their most successful song in British charts, but it peaked only at #78. Even their most successful song Your Love peaked only at #83.
Perhaps the most underrated Progressive Rock band. Although they had some American success by some degree (yet lacked success in their homeland, Germany), they never became as big as other Progressive Rock giants like Yes or Pink Floyd.
10) Wang Chung
A quite unusual case for a Synth-pop band. Synth-pop was always more successful in the UK than in America, but in Wang Chung's case things were different. Can't explain why they lacked success in their homeland, but luckily for them they found success in America with three Top 10 hits (Dance Hall Days, Everybody Have Fun Tonight & Let's Go)