At or near MSRP, I'd likely go with the Tamron the IQ is close and the AF is good, I'd consider it one of those 90% of the lens for half the cost deals. If you can get a 70-200 on big sales like there was in December, then I'd say L Mk II; it is a better lens and when the cost difference is mitigated it is much more attractive.
I love my 135, the 70-200 L IS Mk III however does see more action than I originally anticipated. I shoot lots of sports, and having the zoom when I'm in a fixed position or not moving as fast as the play, make the world go round for most events, in extreme low light the 135 still comes out though. Where the 135 sees more use is in shooting portraits or sometimes in family situations where I know I'll be able to move around. As a parallel to weddings, which I don't shoot so throw in a bag of salt to this comment, I could see the 70-200 being handy during ceremonies and receptions, while the 135 might come out for the group and portrait work, where the 70-200 would still be capable, but the same. Only you know how you work in those variations on a situation.
I do keep the 135, but in adding the 70-200 I also was able to take advantage of one of those ties for lowest price deals, plus rebates, plus gift cards just after the holidays; and I have an f4 version to list that it's replacing, once that is done, the net cost makes the justification a different game. And cost is ultimately a factor. If you're open to used, there's also the IS MkI and the non-IS 2.8s from Canon that are optical winners. And keep an eye on the refurbished sites as well (Canon, B&H and Adorama all have Refurb sections with good reputations)