Yes, the Brit. mode gives you a bit more "hair" as you say, mainly when the amp is on 15W and the gain is around 1:00 or 2:00 o'clock (I love this setting !). If you really want a clean, clean tone, try the USA mode with the 50W setting and ajust the EQ to taste. Try to keep the gain as low as possible, even with the 15W setting, you can have less "hair" this way. And bringing the guitar's volume down a bit will help also.
And no, the Brit.-USA button does not work with the gain channel.