If I ferry an aircraft to the United States (from say the UK) is it a commercial or private flight?
This question was answered in an earlier (2013) message.  

Generally, if you are ferrying an airplane and are compensated as a commercial pilot, are not carrying passengers or cargo for hire, you are operating under Part 91 of the US federal aviation regulations.  That you are a paid ferry pilot is not relevant.  

See 19 CFR 122.1(d) A "commercial aircraft" is any aircraft transporting passengers or cargo for money or other consideration.

As you are not transporting passengers or cargo (both of which would be covered under the commercial operator rules) or you have a passenger as a friend or the aircraft owner who does not pay for passage, you are ferrying an aircraft which is covered as a private flight.

Make absolutely certain you understand how the US eAPIS system applies to you as a foreign national bringing the aircraft into the US, and you have appropriate documentation and the owner is prepared to jump through whatever hoops Customs needs to get the aircraft ashore.  The US Customs Guide for Private Flyers is a useful reference.

Simon, I disagree with your understanding.  There are many operations which are not commercial, with paid pilots.  An example of this is a corporation owns an airplane which requires a pilot.  The corporation can hire a pilot to fly its airplane and carry its parts/executives/employees/friends.  While the pilot must carry a commercial certificate and carry at least a Class II medical certificate, the flight is not considered a commercial flight, nor is the the company considered a commercial operator since it does not hold out its aircraft for hire, unless its in the air carriage business.  If on the other hand that same aircraft owner decided to carry the company next door's freight and executives and charge them for it, that changes the story.