Primes in general are sharper than zooms - or at least that USE to be the case. These days you can't go by that general rule, you have to get specific.
For instance the 70-200 f/2.8 Mk II is every bit as sharp as most primes in that same focal range. The 24-105L is not quite so good.
For portraits the place to start is not with the lens but with the desired distance. You want to be 3-5 paces away from your subject. Now that you're the right distance away, what sort of shot do you want? Full body, head & shoulders, tight face? That is what determines your focal length.
If you have the $ and can handle the weight the 70-200 f/2.8 IS Mk II is probably the best solution. I see you have the non-IS version. I'd go with that. It plenty sharp for portrait work, provided you nail the focus.
The only real optical advantage of the prime is the potential for shallow DoF due to fast apertures like f/1.4 or f/2. Be careful though. At those wide openings, it is all too easy to have too much of your subject out of focus. When I'm shooting people up close, I'm usually at f/4 or f/5.6. DoF is just too shallow at wider apertures for it to be reliable.
Specifically, the 85 f/1.8 is a great portrait lens. 85L may be better but is not cheap. Sigma's 85 f/1.4 is another great alternative. My 85 f/1.8 is sharper than the Sig 85 I had but most report the opposite.