So, we have a 2012, with c.19k miles, that seems sluggish to start....when compared with your previous 2007 FJR. Can we assume there are no codes showing on the dash?
My first reaction is 'they all do that ,sir'. It's 2 big pistons, firing at 270, so apes a 90 v-twin. Like many big twins, Yamaha used an automatic decompressor system, where one exhaust valve on each cylinder is held open briefly, so the starter can spin up the engine initially. This seemingly slow spin up, with no instant bang, can seem strange at first.
Others have covered the battery/solenoid/connectivity questions but, being a 2012 gen 1 bike, there are a few other issues that may deserve investigation if you find yourself in an actual hard start situation. Firstly the CCT - has this been upgraded? If not, then it is possible for the CC to jump a tooth on say a cold start. Rare, but it happens. Secondly, has any significant service work, such as a valve check, been undertaken in the recent past. Finally, have the throttle bodies been balanced correctly - make sure the balance port cap is in good condition, not degraded/leaking.
Then, unrelated to the starting issue - while you are digging into background & service records, is there evidence that the headlight harness has been upgraded. You may need to talk to a Yamaha dealer, as OYB no longer carry the franchise. Then, some owners of early bikes have problems with the clutch basket, which can cause vibrations at certain engine speeds - many will have been replaced or upgraded, but they don't come cheap.
Hopefully you are worrying over nothing - there is a massive info base available with the 'search' function, or just ask away on here.
