Is that the case with all GE turbofans ?
I believe so - and CFM as well (at least all the GE/CFM that I'm aware of).
There are a number of pluses and minuses for both EPR and N1. One really nice aspect of EPR is that, below corner point temperature, Max EPR is basically constant, while N1 varies with temperature ("Corrected" N1 is constant, but then you need to apply that square root of theta term). Even with our fancy computer driven aircraft, some people still foul up the physical versus corrected N1. Thrust vs. EPR is also less affected by high humidity than Thrust vs. N1. Thrust/N1 is also very sensitive to fan damage (e.g. FOD or birdstrike), EPR less so.
On the other hand, N1 is a simple measurement, EPR much less so as misd-agin pointed out. Inlet probes freeze (we've had big problems with EPR inlet probes icing up in Ice Crystal Icing) or get blocked with all sorts of debris (we had an issue several years back with Singapore - they were getting flower pedals in the inlet probes of the 747 outboard engines
). The exhaust pressure probes can also get plugged with carbon, and of course there is always the issue that pressure transducers can drift. Also as Turbine D notes, with modern engines the vast majority of the thrust comes from the fan, so the relationship between EPR and thrust is getting weaker.
There has been a lot of work done on a 'generic' thrust setting parameter - something that would simply go from 0 to 100 - 0 would be idle, 100 would be max rated for the conditions. Although it works great 99.99% of the time, it has some unlikely but nasty failure modes that have discouraged it's use (at least at Boeing).