I have directly compared both, maybe two years ago: Earmax Pro and Naim Headline with Naim PSU. I prefer the Earmax.
Naim has a reputation as being very concerned with dynamic impact. This PRAT thing: pace, rhythm and timing, I guess. And in this regard, the Headline does very well. But the Earmax has an ease and naturalness to it, that is probably only achieved with tube amplification. It is simply more musical, fuller, warmer, with more ambient and low level information. Bass might be the only area where it is getting close between the two: The Naim has great control there, but the Earmax, that is certainly no slouch in the bass either, has more timbre and elasticity, which is especially noticeable with bass violin.
The Earmax Pro is musically more satisfying, without this fatiguing solid state glare. To my ears, the Earmax Pro is simply captivating. I own one.
And somehow I remember the Naim Headline being more expensive. Isn't it?