I have owned a Kawasaki Concours and I now own a '15 Versys 650.
First off, I know that there are a lot of Concours owners out there that love their bikes, and I am not trying to offend them. This is just my opinion:
I like the Versys better in every way. The Versys is lighter, more nimble, quieter, better brakes, better handling, more comfortable.
The Concours had a large amount of engine noise which drove me crazy. The brakes were adequate, but my Versys brakes are much better.
The Concours bodywork was a PITA to remove, the Versys is relatively easy.
If you are going to put the Concours on the centerstand, you better look like Schwarzenegger. It is very heavy and a B***ch to put on the stand.
The Concours is very heavy to maneuver when pushing out of parking spaces. You will learn to back into parking spaces when you park.
The Concours was heavy handling and does not remotely compare to the Versys.
I found the Versys engine to be smoother and less vibey than the Concours.
The Concours is a mile wide with its cases on. The Versys 650LT is much narrower.
I agree with the other posters about riding the Concours first. I predict that you will decide to keep your Versys and it will not take you long to decide.