I have owned both, and I have shot weddings, engagements, and other portrait work. I am not a full time professional. Now you know where I am coming from.
For you, I would certainly get the 70-200mm f/2.8 IS MkII. Why? Because it is extremely versatile and extremely good quality in all aspects. When you are at a wedding, you can use primes to get great bokeh or when the lighting is so poor you have no other choice, but the versatility is really going to be the killer here. I've shot weddings with both a 135L and a 70-200L on separate occasions, and I much prefer the capability to zoom and not have to move my feet to get the framing I desire. I don't like disturbing the ceremony or even dinner guests to "get closer". I would rather zoom in a bit to get my desired framing from further away if possible, or even keep it at 70mm if I am closer. The 70-200 in question is of excellent optical quality, and the IS really is an outstanding feature to have for a wedding. People are moving, sure - but I don't use a tripod for anything either.
For me, I prefer the 135L as my lens of choice. Why? Because of the additional full stop of light, it is lighter weight(1.8lb lighter), more compact, and it is black(not white or terribly flashy in public). I don't shoot weddings any longer, and when I go out to shoot, I want a smaller more effective kit. I bring the 135L + 1.4xTC, giving me both the 135 focal length at f/2, and 189mm at f/2.8. Even at 189mm I find the lens to be great quality, and the tradeoff of not bringing an extra 2lbs or so is huge for me. Do I sometimes miss the versatility, yes, but not for non critical casual uses. If I'm not in front of a client or in a church shooting, the versatility of a zoom is much less important at least for me. I do shoot some sports with this setup, and still find it very useful. I do not shoot any wildlife though.
As others have suggested, you likely will find a place for both in an event photographers kit. I would start with the more versatile 70-200 though, and if you find yourself looking for that one additional stop of light, or even more creamy background bokeh - then you know what to buy next.