Both developers are great. Are they the two greatest 3rd party developers for PC-Engine? Maybe Falcom has to get throw into the mix, but Irem vs Naxat is a clash of titans.
I think that R-type, particularly the original, gives the nod to Irem.
Of course, I totally love Image Fight so maybe I'm biased, but really I think R-Type is a signature release on the platform that really showed off the power of the PC-Engine soon after its initial release.
No mudlinging intended though... Naxat gave the system a lot of great games as well, with the pinball crash/crush games being perhaps the most signature.