Well, you must, according to US law, use your US passport to travel to and from the US. I am going to Canada at the end of this month for a week and because I need to transfer in Boston I shall still have to use my US passport to enter Canada.
I became a UK citizen after being granted ILR in 1998, which followed from a 4-year work permit granted in 1994. I find that being able to vote, serve on a jury, and carry a UK passport is worth it.
The downside of being a dual citizen is that the US continues to tax you even when you are domiciled in the UK. This is difficult to swallow, as only the US, the Philippines and Eritrea tax their expatriates. I shall be spending some time at my company's NY office this year and my tax affairs will become horribly complex because of that.
Good luck in your quest to become a British citizen.
Chris Hansen
http://www.hansenhome.demon.co.uk