The only reason or advantage is size IMO. You will almost always get better end results with more patience and a dslr.
I changed (away from a Canon 5D to MFT and then added Sony A7) for the saving in bulk and weight but now that I've been using CSC's for a few years I think that there are other very valid reasons to change from DSLR's so I'll try and list them...
1 - WYSIWYG. No more chimping and reshooting, see No.2.
2 - The in view exposure, dof and focusing aids, you get the shot right first time much much more easily and more often.
3 - The focus accuracy. No MA and no DSLR variability from shot to shot, focus is just bang on pretty much every time and all the time.
4 - The lenses are often sharper than DSLR lenses at wide apertures and even when wide open.
5 - A CSC is much easier for using manual lenses on, if manual lenses float your boat.
Even if there were no bulk and weight savings I'd still have moved away from Canon if I'd realised the advantages but I think you have to try the gear to see if the advantages work for you. For what I use a camera for my CSC's are far superior to any DSLR I've had and more enjoyable to use too.
Fuji seem to be getting all the love but I think that anyone moving to a CSC should at least take a look at the FF Sony A7 series or maybe even the APS-C A6xxx series. My first generation A7 is the best camera I've ever used and the image quality is outstanding, it's very compact too with my 35mm f2.8 or 55mm f1.8.
There's always MFT too for the maximum saving in bulk and weight and surprisingly good image quality up to high ISO's.
