The (to be) proposed European Leisure Pilot's Licence - we had lobbied hard for it to be called Light Aircraft Pilot's Licence but the politicos overlooked by mistake (grrrr...) the final amendment - will be sub ICAO. For all categories of the ELPL, aeroplanes, gliders, helicopters, balloons, it will be sub ICAO in respect of the medical which is very close to the UK NPPL as regards the medical standards. For the glider ELPL that is the only element that is sub ICAO. I can't recall off hand for the ELPL(A) what other elements of the training are less than ICAO, but ELPL (A) is broadly based on the UK NPPL syllabus for aeroplanes.
The full EU PPL(A) will be the ICAO complaint licence and therefore it should be the one for flying N reg in the EU, I guess. Whether or not the ELPL (A) will be valid for flying N reg I don't know at present. Logically it should be for N reg up to 2mt MTOM (see below), but that would be a matter for the FAA primarily. There are regular meetings between EASA and FAA over regulatory matters and this may well be on the agenda for such meetings. Time will tell.
The ELPL (A) will be valid to fly an aeroplane which is within the scope of EASA airworthiness regulations (less than 2 mt MTOM, non-commercial operation, and other than Annex II aeroplanes outside the scope of EASA) within any EU member state.
All will be revealed next week (probably) in the NPA on the EASA website.
Hope that helps.