I've noticed in my V Rod research that a lot of people are recommending later models due, partly, to the fatter tires.
Is that an aesthetic thing or a performance thing?
I'm guessing "aesthetic". Some people hate the look of fat tires as part of the OCC "backlash". I have not made up my mind which I like better-I always liked V Rods, but never really looked closely at them until now.
If you have to ask what the desire is for a fat rear tire then obviously you don't desire one, so buy something without one. As to your other question, I would say the fatter tire gives an advantage on launch in the quarter mile but handles worse in the curves than say a 180. So if handling is more important to you get either a used VROD with a smaller rear tire or if you REALLY like handling buy something else altogether.
I am not familiar with the "OCC backlash" but I live on a rock in the middle of the Pacific.
Its a looks thingy. Guys will argue about 5HP and adverse handling, and ride quailty. It all comes down to looking cool and nothing says badass sheep like a 240.
2007 VRSCDX the rarest of the DX one year only 1130cc.
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Yes it looks, most all of this is about looks. The 180 tire will corner a bit better than the 240, the question is does it matter to you and does the bike have enough lean or engineering that it actually matters in real situations and what are your riding habits and/or skill level. Also wet weather conditions are less favorable with more rubber on the road. For everyday riding and most street conditions the 240 will make you feel secure, handle crappy roads, uneven road crap, cracks, ect. a little smoother. 240 cost more too!
Basically the 240 other than CVO or SE models, has been around on stock bikes since 07 and I believe you'll have to go with an 08 or older to get a thin tire bike. Not sure when the 240 became standard.