I've got the 85L and would agree that it's not the fastest AF lens around....being aimed at portrature, it doesn't need to be. If you're buying secondhand then I would suggest a MkII as the AF is 60% faster than the original MKI version.
One quirk of the 85LII is that the MF/FTM focussing is a "fly by wire" system rather than the traditional directly coupled MF. The slight downside of this is that the MF is following a little behind your command moves and there is a perceivable delay in the lens reacting.
For catwalk and weddings AF speed shouldn't be an issue but the DOF at f/1.2 might be restrictive for catwalk shots...especially if more than one model need to be in the shot...not sure about that one. The AF using f/1.2 in low light venues should be a benefit but I would expect to use a smaller aperture for the exposure.
If you need anymore info or have questions then I'll do my best to answer although I don't use it in these fields.
Bob
PS...which body do you intend to use this on?