Having just got my US Citizenship in Sept 08, I specifically talked to the CIS officer about this subject. She made it very very very clear to me regarding this. She told me that the USA takes a very dim view of anyone leaving and entering on anything but their US Passport and if you get caught (which would mean that Immigration would have to know you have two passports) you could be detained.
As I understand it this is how it goes.
Return Tickets from the USA to UK and back to the USA, you would have to use your US Passport on leaving and your British or US Passport on entering.
One way ticket out of USA, use you UK Passport as the USA would require you to buy a return to prove you are not staying illegally in the country you are flying to.
If you are flying out of the UK on a return ticket you use your UK or US Passport to leave and your US to enter the USA.
If you have a one way ticket, you have to use your US Passport otherwise you will be required to buy a return ticket to get you back from the USA.
I'll give an example.
I was staying with my DH before we got married and I had to leave the county every 90 days. We bought return tickets Washington-Dulles to Paris and then to come back to the USA (Washington also). Paris would not let me check-in or let me board my flight to the USA until I bought a return ticket out of the USA. I wasn't even using an American Airline, I used Air France. I bought a full price refundable ticket and had it refunded at the US Airport when we landed. Just as well we had a credit card with us.
I guess once you have Dual Citizenship you can use them how you wish because you can prove Citizenship to both countries. I would never fly without both my passports. You have to use the passport from the country you are entering most definitely. I was just told that the USA would prefer Dual Citizens use their US Passports while on American soil which would mean leaving also.
Problems only come when you fly one way, you would need to prove your are a Citizen of the other country or you at least have a visa for the country you are visiting.
Why would anyone fly one way when it costs way more.
I say do what you want........just never fly without both of your passports, always take both passports.....ALWAYS.