I'm a huge proponent of making decisions based on measurements (I've taken 40+ measurements of my HT room in the past 4 days) but it's equally important to be wary of being dictated by measurements.
An amp may be very accurate, but that doesn't mean you're going to like the sound coming out of your headphones with that amp. You may actually prefer a less accurate amp based on what your headphones do with that signal. You never actually "hear" an amp; you only hear what your headphones do with the signal coming out of that amp. Because no headphone is linear, you're not going to hear anything "accurately" even if your amp is very linear.
An accurate amp might show you what your headphone's biases (some of which you might consider weaknesses) are, but you might prefer that your amp modify those biases/weaknesses, which is why so many people love different kinds of amps (tubes, op-amp, etc) that are not so precise (any vinyl lovers out there?). I love the very non-linear-to-my-ears Monoprice Liquid Gold X amp paired with my Focal Clear because of how they interact; it sounds way different from a solid-state like the Topping DX3 Pro. But I ultimately chose what I consider to be a more "accurate" amp, the Burson C3XP, because I preferred that sound for the long run. Accurate is a good reference to be sure (perhaps it's the only possible reference), but achieving it may not make you happy. (Case in point: the majority of people prefer a 3-6 dB bump in bass above "flat" in a home theater situation, but who cares if it's not "accurate" or if the bump is coming from the amps or the speakers or your speaker's positioning or your room or whatever.)
Critically compare an "accurate" vs. "not accurate" amp with your headphones and make the choice for yourself. You have to live with your investment, not anyone else.