EM1 or D600, for Weddings?

First, size and weight is a huge advantage at an event where you have to be very mobile. I carry one camera bag with two complete E-M1 systems, including flashes and spare batteries -- plus a tripod and monopod in a separate bag.

Here is an example of why that is important. A couple days ago I shot a large professional association event at a local resort. Coverage included early morning registration and breakfast, the opening session in an adjacent ballroom, break out sessions in various conference rooms spread around the resort, coverage of a golf tournament, coverage of a tennis tournament, coverage of a cocktail reception and awards banquet and dancing. I started shooting at 7 AM and finished at 10:30 PM.

In every situation mentioned above, I needed to have back up equipment at hand -- not stored at some remote location. I could not possibly have done what I did lugging two FF systems around with me.

Aside from size and weight, here are other advantages --

WYSIWYG viewfinder allows me to see my exposure, settings, and WB in real time -- a big advantage when shooting ambient light exposures in different conference rooms with different types of lighting. You can make fast adjustments on the fly, before missing an important shot.

The ability to switch to 'Live view boost' so that when shooting in a very dark or back lit situation the viewfinder gives me a bright, clear image of my subjects -- this comes in very handy for ballroom dancing where light levels are extremely low, or when shooting subject against an extremely bright backlit situation like a sunny window.

CDAF AF -- which is extremely accurate in low light situations. Again, after shooting about 100 low light dance exposures I had a couple that were clearly OOF, which I was able to delete on the fly. Everything that looked in focus on my LCD, was in focus -- PDAF in low light tends to produce a number of exposures that appear to be in focus, but are slightly OOF, requiring PP sharpening time and effort.

Very fast AF/shutter release when using Live View. Mirrorless is very fast, DSLR's are still much slower. Again, important e.g. when you are doing a shot in Live View with camera held above your head -- for example at a reception dance.

I could go on, but these are just a few advantages for me for the type of shooting I do, and would also be advantage to any wedding photographer.