If you throw out the NAD, which really is not in the same category as the Hegel and Gryphon. Then you have to try to understand the seemingly contradictory comments between “they sound the same/similar” and “they are wildly different”. You are getting honest recommendations from different folks. So, one must look elsewhere to understand the difference.
My way of looking at this common problem comes from experience. I have been pursuing the high end for fifty years. As I have progressed, I have learned, both in how to listen and evaluate. The reason many folks find this pursuit so fascinating is that it is so nuanced and deep. You can learn layer after layer, for a lifetime. As your listening skills get better, your ability to appreciate and hear nuances becomes much better. Audio equipment is much like scientific instruments… the better they are, the more detail and nuance they get correct.
When you get into audiophile level gear from respectable companies you get what you pay for. Lots of the real satisfaction comes from what you don’t know when you buy it, but come to know after you own it. You learn to listen deeper and enjoy more. This is why you would buy an integrated that was twice as much. Over time you will discover nuances that you had no idea existed when you bought it.
I am reminded of a number of components I bought when I started off (used and relatively inexpensive) and suddenly became aware of a shortcoming that I had read about, for instance grainy treble. I remember a week after buying a used preamp that I thought sounded great, and suddenly (think a curtain of red dropping over my face) hearing the horrible grain in the treble… I took the unit back… loosing $250 (in 1978) in the process of trading to a used Audio Research preamp that I loved and cherished for nearly twenty years.
Great audio components teach you what is right, lessor ones show you what is wrong.
I am reminded of the Big Bang episode when Sheldon sets off to perfect scrambled eggs… after trying all sorts of variations of sizes of eggs, and ways of cooking, he concludes… there is nothing there… we do it just fine. Kind of the opposite of high end audio.