I don't have experience with a VTX 1800, but I watched the Rocket III since the first rumours started about it's existence. I tried to resist. I owned a Thunderbird Sport at the time it came out and as much as I love that bike, and I still miss it, I couldn't make it be as much of a long distance cruiser as I would like.
So, even though I visited almost every Triumph dealer in Texas drueling over Rocket IIIs, I went and sold my Thunderbird Sport and bought a..... Road Glide!!!! Now, don't get me wrong, the Road Glide was a great bike. Awesome tourer, but it had two things against it. It wasn't a hot rod.. and it wasn't a Triumph.
I owned the Road Glide for 6 months... I picked up my Rocket III this past New Years weekend and have never looked back like I did with the Road Glide. The Rocket III is a very versatile bike, fully capable of long distance touring, or being the hot rod bar hopper, or for a large bike, it can handle the twisties very well... I love it.. It's a true, all-in-one bike for me..