There is nothing you cannot do with an FAA PPL in NI, you can do more, actually: Fly at night without the extra NQ, fly US registered aircraft in the Europe, no expiry date, cheap medicals (in Dublin for example, but quite possibly in Belfast too). I have heard that there is a restriction with regards to crossing borders (as BP mentioned), but could not find the reference, so if someone has it, I stand to be corrected.
As far as crossing borders is concerned, it isn't so much an explicit restriction, as something that's not explicitly allowed.
Here's how it works. Every state in this world, in principle, requires that every person coming into the country requires a passport+visa, every item coming into the country requires import duty, and every person in the country needs to comply with local laws and regulations, including licensing. Obviously for international airline travel this is a bit cumbersome, to say the least, so at the Munich (?) convention all countries that are member of ICAO have set a number of rules on recognition of foreign licenses and other documentation.
The rules basically specify that if a pilot holds a license issued by country A and flies in an aircraft registered in country A (within the limits of his license, and while complying with all the relevant regulations of country A), then all other countries will accept that combination without further problems. Since all JAA countries have mutual recognition of each licenses, this also applies to a license issued by A on an aircraft registered in country B, where both A and B are JAA countries.
This privilege does NOT automatically extend to flying an aircraft registered in a JAA state on a non-JAA license (FAA in this case). The UK CAA considers an FAA license good enough to fly a G-reg up to PPL level/privileges (that's explicitly mentioned in the ANO), but other countries do not necessarily share that same view. So if you ever crossover into another country in a G-reg on your FAA license, you have to ask permission to do so from the country where you'll be flying in. This probably will not be a major issue when it concerns only PPL privileges, but it is an additional hurdle. One you will not have if you fly an N-reg on an FAA PPL, or a G-reg on a JAA PPL.