I'll try to keep this short:
I have done endless simultaneous Audio/MIDI re-record tests with various versions of SONAR over the years. Based on this experience, I can tell you a hard-quantized MIDI track rendered by a soft synth that does not itself introduce timing/sample/amplitude variations will play back with sample accurate timing and consistency from one playback to the next. As others have said, this is what most of us want. If any "magic feel" needs to be added to a part, I'll take care of it. I don't want my DAW or my synths doing anything but what I tell them as far as MIDI timing goes. If the synth is randomizing samples or otherwise adding dynamic or timbral variation, that's different. I'll also make a special exception for layered sounds where some random phase variation between layers can help enhance the "liveliness" of a sound without being detectable as a timing variation.
In my experience, the natural variation of note velocity and duration you get from recording a live performance is
way more important to the musical feel of a MIDI part than variation in start times. Although I don't, usually, I can hard-quantize anything I've recorded live from a keyboard/controller, and it won't make the part sound nearly as stiff as you might imagine. So long as the synth has a smooth response to velocity with both dynamic and timbre variation, and the durations are not quantized, it will continue to sound quite natural. Conversely, quantizing durations and/o or flattening velocity variation will instantly squash the life out of almost any MIDI track, regardles of how "groovy" the timing is. Of course, the duration element does not apply to one-shot drum samples, but the dynamic and timbral responses to velocity are crucial.
Only a blind test with as many possible variables eliminated as possible - like the ones suggested - can rule out subjective factors in what you're hearing, and identify real differences. This isn't "making it about the person"; this is just how it has to be done when you're trying to answer questions about how "musical" a performance "feels".
And just for the record, at least three of the contributors to this thread don't need any MIDI history lessons; we were more or less present for the birth, as it were.