I have used the 100 L lenses for a few years now, only on Underwater Macro, the non IS Lens was good, but the newer L IS Lens is simply better all round, lighter, sharper & the IS does count, I cant give you technical reasons why, but in my Underwater Macro Photography the L IS 100 is a great Lens. I am also using the D800 with the Nikkor 105, also a good Lens but not as good as the Canon 100 L IS.
On the f/4 70-200 cant comment as I've never owned one, but I do have the 70-300 L & the 70-200 f2.8 L IS V2, the 70-200 v2 is simply one of the best Lenses I've owned, sell your car & buy this Lens, you will appreciate the f/2.8 over the f/4 I am sure especially as you mentioned "Weddings", never shot a wedding biut I imagine the low light benefits of the f/2.8 would be superior for this sort of work compared to say the f4 to f5.6 of the 70-300L. The 70-300 L is not a bad lens, Good range reasonable IQ, but not in the same class as the 70-200 f/2.8 L IS V2 Lens & it is shorter & lighter than the 70-200 v2, I rarely use the 70-300L anymore, bought it for Safari shooting but the slow speed kills it for dawn & dusk shooting, works good in brighter light though & the other disadvantage with this Lens is you cant use the 1.4x or 2x extenders, so your stuck with the range.