Thought about renting both lenses to do a head to head? They're so close in many ways, that often times, it's the subjective character stuff that matters.
The 85 ART again is easily the best affordable AF 85mm on the market right now, wide open. But, that doesn't mean it's the best 85mm for someone.
I too use 85mm for portrait more than anything. I had to juggle 3~4 85's for a while. I was using an 85mm F1.4, the 85mm F1.8, a 90mm F2.8 VC macro, an 85mm F2, etc. The 85 F1.4 was sharp wide open, loved it. The 85 F1.8 was sharp and super fast AF, enjoyed it. I ended up selling all of them and only kept the 90mm F2.8 VC macro lens (basically an 85mm F2.8 with macro distance focus, fast focus still, weather sealing and 4 stop image stabilization). I very often shoot my portraits with lighting. So I'm commonly using F2 and F2.8 a lot, so I found I just didn't need the F1.4 anymore and let it go. Even in natural light, I don't need to obliterate backgrounds, I like a soft background, but not something totally obliterated. So ultimately I let go of all my 85's and kept the 90mm F2.8 VC macro. It's fast enough to focus on a running kid, so I don't miss the 85 F1.8 AF speed. And it's tack sharp wide open at F2.8 so I can shoot it wide open. So for me, the Tamron 90mm F2.8 VC replaced my 85's and macro needs and does triple duty. But that's just how I went with things.
Later I added a 135L to get that "obliterate the background" thing going and immediately felt the the working distance issue, as I don't like being that far from the subject, so I still prefer 85mm working distance over the 135L by a long shot.
Personally, having used image stabilization on portrait lenses, I actually like stabilization over focal-ratio because I have more creative options with slow shutter speeds, in natural light and with lighting, because I can successfully drag the shutter in lower light.
When I look back at images I did with my various 85's, I can definitely tell which one was the F1.4 because F1.4 obliterates backgrounds more than the 135L does by a little bit. But I can't tell the difference between my other 85's and my 90 F2.8 as the DOF difference even at F2 or F2.8 isn't so starkly different that I gravitated to one or the other. Ultimately I went with what was more versatile and flexible and offered me more options, which happened to be the one with image stabilization and more focusing options (macro).
I too am looking all the time at 85's. None of the newest fast primes interest me though, not even the Sigma ART, despite it being super good. I'm more interested in the 85L with IS and the Tamron 85 with VC because I'll take image stabilization for the long run as an option over not having it, as it opens different doors for creative portrait/lighting work. But that's just my take.