I'm sure you'll get answers that clearly validate both choices. As for me, I went with the 6.5" and could not be happier.
With the Raging Judge Magnum, let's face it -- short or long barrel, it's still a preposterously huge revolver! So, in that context, I figured -- go big or go home, right? If it's already a five-pound gun, might as well have the longest barrel you can get -- that longer barrel will make it more powerful and more accurate. In comparing the two, the choice was also pretty easy for my situation. I already had a Public Defender, so I already had a short-barrel Judge.
I've found the Raging Judge to be very, very accurate. The long barrel puts a lot of distance between the front and rear sights, such that it's very easy to shoot very straight with it. On my first outing with it, I took a shot at the "5" on one section of a target, from 25 yards out. This is what I hit.
Now, sure, someone might shoot better, but I was pretty pleased with that shot, considering it was freehand, from a 5-pound gun, and 25 yards away!
Yes the longer barrel makes the gun huge, ridiculously huge, but ... it's always going to be huge no matter what; it's not like a Raging Judge is a concealed-carry firearm. And yes it's heavy, but the question is whether you need to shoot the .454 Casull round or not. If you need the .454 Casull, then you may find you actually prefer the heavier longer barrel, since the recoil is rather severe and I can only imagine that the lighter, shorter-barrel version has worse recoil. It's pretty amazing how the heavy RJM tames the recoil of 45 Colt loads; they pretty much feel like shooting 22LR's since the gun is so heavy and it soaks up the recoil really well. But the .454 Casull rounds have substantial recoil. So the question is -- if you don't need the .454 Casull, maybe you'd prefer the Raging Judge Ultralite, which is a 7-shot model that's a pound or two lighter, but can't handle the Casull. I'm sure it would still be every bit as accurate as the full-bore heavy long barrel model, and it's big enough that I'm sure it absorbs plenty of recoil. If you want the huge power of the .454 Casull, don't get the Ultralite model, as it's not chambered for it.
The longer barrel may also give the option of mounting a scope or red dot sight. Taurus makes a rail for the Raging Bull that may be somewhat adaptable to the RJM with a little bit of machining, so if you wanted a scope, you'd want the longer barrel.
Anyway, those are a few reasons I think the longer barrel is well worth it, but as always, only you can decide what's best for you.