Keep in mind this is a very simple explanation of steering.
Steering on any motorcycle is a compromise between overall wheel length and the rake and trail of the front end. The shorter the wheel base as with sportbikes, or the steeper the steering head angle (steep rake, less trail) the more unstable or faster turning the motorcycle. The twitchy-ness is more noticable at speed then when moving slower. Sometimes it will feel like the bike "falls" into the corner.
The FJR has a longer wheel base then most sportbikes in general, is heavier, has more trail and less rake (less steering head angle) then a sportbike. Therefore, it steers heavier, turns in slower and is more stable at speed.
To figure out how much trail you have or to compare from bike to bike, draw a line straight down the fork tube to the ground and then measure from that point back to the center of the front wheel contact patch. That distance is the trail. It is measured in millimeters. (this is a rough approximation)
All of this ssumes that you have proper tire pressures and sizes mounted up on the bike. Another thing that will cause changes in feel is the changes that happen when you change tire brands. Not all tire are the same size even thought they may say they are 120/70-17 or 180/55-17. The overall hieght and circumfrence can be different. For examply on my Honda RS 250 GP bike, I would switch occaisionally from a Dunlop slick to a Bridgestone slick. In the rear the Bridgestone was 10mm taller. The circumfrence was larger too. This affected the suspension and gearing for the bike drastically. There is a good article by Ed Sorbo (long time AMA pro racer and mechanic) in the March 2010 Roadracing World magazine that talks about all of the effects that happen to a motorcycle from a simple thing like changing tires. Tire profile can also have a great effect on steering. In the above example, Dunlop front tire slicks had more "triangle" shape, which aids the feeling of falling into the corner. Where the Bridgestones were rounded in profile and had more of a smooth transition into the corner.
EDIT: my point is to illustrate there are many more things than just tires that affect how the bike handles