The 70-200 2.8 IS version 1 that I had was wonderful as a portrait lens on my classic 5D when shooting wide open and the bokeh was also beautiful even stopped down to 2.8 through 3.5 when shooting at focal lenghts between 135 and 170mm, I loved that lens for portraits on my FF. But I had the 85L during that time as well and really didn't like using it, I personally don't like to go shorter than about 100mm equivalent when doing head shots but what really bothered me about the 85L on my 5D classic was that the focus was so slow and bad in the outer focus points which I always used when shooting head shots. I almost sold the lens as I had stopped using it because of too many missed focus shots. I love to use that lens wide open at f 1.2 through f2.
Then I got a MKIII and the 85L 1.2 skyrocketed to #1 favorite for portraits, the focus is fantasctic with that camera, the additional focal lenght equivalnt on the 1.3 crop is really a favorite and I passed off my 70-200 2.8 and replaced it with a 100-400 for more outdoor shooting since I didn't appreciate it as much for portraits. Yes it did turn out beautiful images but I prefer the 85L and also use it a lot for other shooting. I tend to carry the 85L and 24-70 with me most of the time now, with the 85L installed on the camera ready to go. I also use both exclusively now for table top and still life work.
But and this is a big BUT, if you are working with a FF camera, it would definitely be my choice and preference to use the 70-200 2.8 for portrait work, I think it's more versatile. The 85L would be wonderful for head and shoulders, it'll do it, I think it was made for that so many will disagree with me but the focus situation really caused a lot of missed shots and I probably used that lens on my FF for at least 5,000 frames because I really wanted it to be the one. Now on my 1.3 it is #1.