You will absolutely LOVE the Triumph Rocket, if you decide to go that way.
As you have previously remarked above; you have sensed her.
I have had my Rocket 3 (2008 Classic) for a couple of months now, and can make a good comparison between it at the 2007 1300R that I still own (and will continue to keep) - (though I know that you asked for a comparison between and 1800 and a Rocket).
You will find that you ride slightly higher on a Rocket, as opposed to a VTX; just have to look at the floorboards and seat height in the dip of the saddle.
The Rocket has more "girth" as opposed to the VTX. Sitting on the Rocket is akin to sitting on top of a Brahma bull's back. No chit
It is rumored that Rockets eat up rear rubber much more quickly than the VTX; which is probably due to more anticipated "twist of the throttle" activity directly rewarded by the power plant which lives within it. When my time comes. I am going to have a car tire installed; I never thought I would do this on a motorcycle but my style of riding and the current 240 that is sitting in the rim of my Rocket is a "no brainer" to me. It needs to be done. Good reviews that I have seen from other Captains that command Rockets with car tires.
I do hope that you are satisfied in whatever you decide on, for your new ride. I sincerely offer to you, that if you decide to own a Rocket III; a new awareness will open to you concerning power and motorcycling.
I still have my VTX. I enjoy it immensely.
... The Rocket III absolutely beats every motorcycle that I have ridden "hands down".
2007 VTX1300R (gone, miss it but not cleaning the the chrome...)
2008 VStrom DL-650 (gone, miss it....)
2008 Triumph Rocket 3 Classic with Carpenter Racing 240hp package
2011 Victory Vision Tourer
2012 Suzuki DR650SE
21 years retired Army - Seen EVERYTHING - Done ALMOST Everything... Ooorah!