I have both a 380EZ and an Equalizer. Measuring with a caliper, I get the Equalizer being about .040 wider at about 1/2" from the muzzle. But measuring at the take-down lever, the 380 is about .015 wider.
So, obviously it's going to depend on the holster. L.A.G. sells the same kydex holster for the 9EZ and the Equalizer. My Equalizer fits snugly in it. My 380 fits nicely but not quite as snug - that's without playing with any of the adjusting screws. I keep the 380 in a nylon holster that won't accept the Equalizer with an optic.