I have both and except for a better T stop, the fact that it is less intrusive and lighter, I see no advantage to the 85mm over the 70-200 II. And the 70-200 II has IS and is better in the sides and corners.
I see no advantage to f/1.4 because I have to stop down to f/2 at least, to get a decent DOF.
I am very close to selling the 85mm, but before I do, I would like expert opinions as to what am I missing, please.
In my opinion, you are quite right about you not missing much, if and when you sold the 85, due to the awesome performance of the Canon (I assume) 70-200 f/2.8 II. One reason you might want to not sell the 85 is the financial loss and the loss of using two camera bodies simultaneously, as in a situation where an assistant or associate would use one while you use the other. And, if you can learn to get the occasional shot focused well at f/2.0 or f/1.4, and don't need sharper corners, well then, that is just the marginal opportunity the lens was designed for.
I am able to use f/1.6 fairly often with my Canon 85 f/1.2, as this picks up just barely enough depth of field for my focus to be more often within the very narrow depth of field. However, the 85 is pretty much limited in strength to its wide open, or near wide open, aperture use, usually as a portrait lens, while the 70-200 is amazingly sharp wide open and can be used for portraits at a variety of focal lengths, plus every other use when a short to moderate telephoto is required. Most of my head shots are done with focal lengths longer than 85mm and shot at apertures from f/4 to f/11, depending on the position of the client's head in the image. On less tight portraits, my 85 comes out of the bag about half the time, but I still shoot mostly in the f/2 to f/5.6 range much more often than wide open, or even at the more forgiving apertures between f/1.2 and f/2. I'd say that my use of the 85 at apertures wider than I can get out of the f/2.8 is at about 20% of the time at most.
Yes, I could sell my own 85 and hardly ever miss it, but, for those rare times, it really does produce some wonderful narrow aperture effects and bokeh, the two areas where it definitely eclipses the otherwise superior 70-200.