Well I must have come full circle here.
I rode a lot of bikes but in the last 15 it was HD, a Sportster which was a girls bike but a hoot to run, then a Road Glide that was my first experience with a frame mounted fairing. Both were great bikes. The Road Glide I had a BUNCH of money in to get to the elusive 100/100 club. Still I ran it anywhere and everywhere and it was a great bike. I then traded that for a BMW K1200 LT. Just a fantastic bike that I loved and ran 30,000 before I totaled it in July.
So I get my insurance money and start figuring what I want. What I wanted was a BMW RT style Sport Touring bike but did not want another BMW.
The FJR was my final choice but I also looked at a C-14. The choice was close but the security on C14 I did not want, as BMW went rounds with Antenna Rings disabling bikes, the C14 had/has issues not letting you start your bike, I would go ballistic and kick it over myself.
I also like the way I felt on the FJR better than the C14. It just fit me better.
So you are going to have to ride them or at least sit them to see how they feel that way.
Then you need to think about how you ride. I have progressed in my riding tastes and style that I am for sure a Sport Touring kind of guy. A Road King is not a sport touring machine, but it is a damn fine touring machine.
None of us can answer what you are asking other then our own reasons for choosing the FJR. You have to choose what your reason is and maybe not even the two choices you mentioned. Go look at Triumph, they make some fine bikes.
On the FJR what I like the most is you do not got to put any money into it to make it run like a scalded dog. A PC V and a set of slip on mufflers will get you all it has and I know I will give up long before the FJR does. I mean in cornering and winding out the gears to top end. I see guys talking about 125, 150 MPH! Not in me, the fastest I have gone on a bike is 120 and that is enough for me.
I hope you find what you want but you are on two different bike designs and functions, so you need to figure it out yourself. I know a Road King or a FJR, man what a rough choice to have to make