I like the big sound and the depth of it, plus the overall balance. It has a strong fundamental tone with plenty of bass, but still fairly articulate midrange sounds too. As you said, it gives the D-28 sound but with some decent mids too. This is a large rosewood / spruce body, now with about 25 years of aging and play time, so it has mellowed nicely. It's kinda like a smooth scotch - once you know what that is like, most everything else seems rather harsh. When I was auditioning my first REAL guitar I played a number of stock J-40's in various shops. The tone grabbed me, plus I am a big guy and the big body seemed to fit me nicely. I was mostly a fingerpicker in those days, and had a very light touch, so this guitar still produced some decent volume without driving it too hard. But I thought the stock J-40 was kinda "blingy" so I toned it down a bit when I ordered my CS version. The back has some really nice rosewood (one of the benefits of going custom shop, at least in those days). The top started out the same shade as a manilla file folder, but has aged into a nice golden tone by now.
Since discovering Taylor, I have always wished for a guitar with that sound, but with a Taylor neck and playability. The most comparable Taylor version would be something like an 816 which comes pretty close, especially in the newly re-braced post 2014 version. The GO models go a bit too far in that direction for my ear, just a touch too bassy.
Now that my J-40 has had a bunch of factory defects corrected by a good repair shop, it plays and intonates better than it ever has - as it should have leaving the factory. The bridge was in the wrong place originally, and I actually had him move the bridge about 1.5 mm further away, telling him to set it up for medium strings tuned down D-D as the normal use. The J-40 really sings at that tuning. I recently experimented with heavy (59-14) strings tuned down further at C-C, so this is guitar has essentially become my "short scale baritone" now.