What class of amplifier has the most high definition sound ?

Audio Research.

Says so right there on the front panel, can’t miss it.........

When I joined the single ended tube amp cult (the meetings surprisingly  require elaborate disguises and often feature meaningless chanting) it was sort of an experiment as I became curious about all the fuss and mythology about these amps, so to speak. The tonal palette revealed in the amp I wound up with, a Dennis Had hand made little 12wpc gem called an Inspire Firebottle HO (high output), was a surprising and simply a game changer. I'd been using a classic push pull tube amp for some years prior to the Had amp, have owned countless nice SS amps, use tubed guitar amps for over 50 years, and still...blown away by the Had. Paired it with relatively efficient (alleged 91db Silverline Preludes, 93db Sonist  Recital 3s) and although preferring the Preludes over the Sonists tonally I was compelled by curiosity (again) to try Klipsch Heresy IIIs with the 8ohm nominal 99db efficiency. Added a tube preamp, and am happily enjoying the rig on another level entirely...tied to efficient speakers, el tubo a mundo, and enveloped in a self indulgent smugness about the whole thing. 

Practically, high efficiency good quality Class D amps are capable of delivering the most high definition sound with the widest variety of speakers.

Otherwise, at the other end of the spectrum, low efficiency Class A amps can do the job very well also but you typically need larger, higher efficiency, easy load to drive, and typically more costly speakers to get the deed done.

How loud one need go is another key factor. A lot of detail listening is done practically  at modest volume, which is a lesser challenge for most amps.

Please define "high definition." I have no idea what is meant by "pure sound."

Though I haven't yet heard one (soon to be rectified), I am curious if the answer turns out to be a direct-drive tube amp driving an ESL loudspeaker. No amp output transformer, no ESL step-up transformer---sounds very promising, right? An OTL driving an ESL gets half the way there, but that designs (generally) somewhat high output impedance brings its own potential penalty.