I have both lenses....
The Canon 85/1.8 is an excellent portrait lens. Its reasonably well built and fast focusing. In fact, the lens' USM AF is very accurate and fast enough it can be used as a short sports tele. It can be used considerably closer by adding some extension tubes, but certainly isn't a macro lens on it's own. As an EF lens, it can be used on either crop cameras or full frame.
A minor complaint I have about the 85mm is the lens hood is a clip on, rather than a bayonet mount. Looking at it, you would think it might be easy to break.... But I've been using the same one for a number of years without any special care and have never damaged it, even though I've bumped it hard enough to knock it off the lens at times. The 85mm also can exhibit some chromatic aberration, especially at large apertures. It's not a lot and usually can be pretty easily fixed in post processing.
I got the Tamron SP 60mm f2.0 recently with the idea of it replacing three lenses in my camera bag sometimes (50/1.4, 85/1.8 and either 90mm or 100mm macro lens). I'd planned to carry it when I didn't know that I'd be shooting macro or portraits, when I was carrying other lenses and wanted to lighten up my load.
I found it has very nice image quality, even wide open. This was no surprise to me, because I've used a number of Tamron SP lenses over the years and they have always offered top image quality. It's a little shorter focal length than I normally use for macro, but its an internal focusing (IF) lens so does not grow in length when focused closer. Working distance is minimal, but workable.... though I don't think I've shot with it at full 1:1 yet.
I've shot some portraits with it and the f2.0 aperture is nice to have at your disposal.
Where I found the a bit wanting is in build... It's a little more plasticky than I expected from past experience with Tamron lenses. To be fair the 85/1.8 is a bit plasticky, too. Neither of them is an L-quality build, but they aren't priced like an L-series either. The Tamron comes with a matching lens hood, where the EF 85/1.8 doesn't (it's sold separately).
Also, the Tamron lens is slower focusing. It's a micro motor drive, I think. Certainly performs like it, though it's not loud like some micro motor lenses and it seems accurate. And it doesn't have a focus limiter like some macro lenses. You won't be using it for sports. On one of my 7Ds it couldn't keep up tracking a 3 year old coming down a slide or on a swing. Other lenses I use could track (Canon USM). I have not used the Canon EF-S 60/2.8, but imagine it's USM is faster than the Tamron, though it's probably not as fast as non-macro lenses such as the 50/1.4 or 85/1.8. The price of the Tamron 60mm vs the Canon 60mm isn't much different. But for my purposes the f2.0 aperture of the Tamron was more important than the foucs speed.
The Tamron is a nice lens and I'm keeping it for a while. It does macro and portraits well. It's a bit of a compromise for me, for macro. So it's a back up or substitute lens when I want a compact and lightweight lens that will take up minimal space in my camera bag.
But I'm also keeping my 50/1.4 and 85/1.8.... I still prefer them for portraiture when possible. And I certainly will be hanging onto my 100mm macro for the additional features it offers (tripod mount, focus limiter, more working distance, and more).