Ah, the sound of a can of worms being opened!
.... but you had to have completed a FAA BFR and have it recorded as completed in your logbook and signed (by a FAA Certified Instructor) if you are flying on the basis of a FAA 61.75 issued certificate
FAA 61.75 states:
Private pilot certificate issued on the basis of a foreign pilot license.
(a) General. A person who holds a foreign pilot license at the private pilot level or higher that was issued by a contracting State to the Convention on International Civil Aviation may apply for and be issued a U.S. private pilot certificate with the appropriate ratings if the foreign pilot license meets the requirements of this section.
[(b) Certificate issued. A U.S. private pilot certificate issued under this section must specify the person's foreign license number and country of issuance. A person who holds a foreign pilot license issued by a contracting State to the Convention on International Civil Aviation may be issued a U.S. private pilot certificate based on the foreign pilot license without any further showing of proficiency, provided the applicant:
(1) Meets the requirements of this section;
[(2) Holds a foreign pilot license, at the private pilot license level or higher, that does not contain a limitation stating that the applicant has not met all of the standards of ICAO for that license;
(3) Does not hold a U.S. pilot certificate other than a U.S. student pilot certificate;
(4) Holds a medical certificate issued under part 67 of this chapter or a medical license issued by the country that issued the person's foreign pilot license; and
(5) Is able to read, speak, write, and understand the English language. If the applicant is unable to meet one of these requirements due to medical reasons, then the Administrator may place such operating limitations on that applicant's pilot certificate as are necessary for the safe operation of the aircraft.
(c) Aircraft ratings issued. Aircraft ratings listed on a person's foreign pilot license, in addition to any issued after testing under the provisions of this part, may be placed on that person's U.S. pilot certificate for private pilot privileges only.
(d) Instrument ratings issued. A person who holds an instrument rating on the foreign pilot license issued by a contracting State to the Convention on International Civil Aviation may be issued an instrument rating on a U.S. pilot certificate provided:
(1) The person's foreign pilot license authorizes instrument privileges;
(2) Within 24 months preceding the month in which the person applies for the instrument rating, the person passes the appropriate knowledge test; and
(3) The person is able to read, speak, write, and understand the English language. If the applicant is unable to meet one of these requirements due to medical reasons, then the Administrator may place such operating limitations on that applicant's pilot certificate as are necessary for the safe operation of the aircraft.
(e) Operating privileges and limitations. A person who receives a U.S. private pilot certificate that has been issued under the provisions of this section:
[(1) May act as pilot in command of a civil aircraft of the United States in accordance with the pilot privileges authorized by this part and the limitations placed on that U.S. pilot certificate;
(2) Is limited to the privileges placed on the certificate by the Administrator;
(3) Is subject to the limitations and restrictions on the person's U.S. certificate and foreign pilot license when exercising the privileges of that U.S. pilot certificate in an aircraft of U.S. registry operating within or outside the United States; and
[(f) Limitation on licenses used as the basis for a U.S. certificate. A person may use only one foreign pilot license as a basis for the issuance of a U.S. pilot certificate. The foreign pilot license and medical certification used as a basis for issuing a U.S. pilot certificate under this section must be written in English or accompanied by an English transcription that has been signed by an official or representative of the foreign aviation authority that issued the foreign pilot license.
(g) Limitation placed on a U.S. pilot certificate. A U.S. pilot certificate issued under this section can only be exercised when the pilot has the foreign pilot license, upon which the issuance of the U.S. pilot certificate was based, in the holder's possession or readily accessible in the aircraft.
Amdt. 61-124, Eff. 10/20/09
Now, where in there does it say that I need to undertake a BFR (now called simply the Flight Review)? The received wisdom is that it's 'safer' to do a FR, one argument being that the above regs only cover 'issue', but that it might not be 'valid' until the FR is carried out. But the back of my 61.75 certificate states: 'Issued on basis of and Valid only when accompanied by UK PPL no......'
Truth is, no-one knows a definitive answer. If you call the FAA, they give you a range of different answers, usually outlining the above. Happy to be proved wrong though.
TTB (well thanks, should be flying today but it's raining and I'm a fair weather pilot!), in theory I think he 'could' fly his N reg all over Europe on his JAA licence. However, I was ramp checked at EBBR last year and they were all over my licence until they found my 'based on' certificate, at which point they were all smiley and happy. So for the cost of a bit of paperwork and a trip to the States, it's worth getting the FAA61.75 certificate. However, a new cert will be required when the JAA licence runs out. I have a CAA licence which is everlasting.