I have white Eneloops bought in various batches over the years and white AmazonBasics (1900 mAh, now black) that I use in devices around the house (AA and AAA for both brands). I haven't tried the current black or silver AmazonBasics, but comparing what I have of the same vintage and rating, my impression is that they are not the same.

The AmazonBasics are better than any of the non-low-discharge NiMH batteries I've used (Maha Powerex, Energizers, and maybe one set of Rayovacs), but not quite as good as the Eneloops (driven home when I was without power after Hurricane Matthew, and hauling my Maha charger and a sack of batts to work every day). How good a deal the AmazonBasics are may depend on timing - when I bought the ones I have, the price seemed to change every few hours, sometimes a great deal, sometimes "meh".