If you are going to be logging some serious playing time with your Rick 12, I would go for the 360-12, in whatever version -- reissue V64 or C63 or newer with hi-gains. It is light and fits under your elbow pretty well for hours of playing while standing.
The 381/12V69, as noted, is more bulky and heavy. The neck width is the same on both models.
The real issue for me with the 381/12V69, however, is that it is such a work of craftmanship and art, you likely will not want to drag it around for gigs. So if you are looking for something that looks super (hold out for flame!) that you will play for your own enjoyment, holding out for the 381 is not a bad idea. If you are doing gigs, I'd go for a 360. My issue with the 330 is that, without the edge binding on the body, it tends to accumulate edge dents and wear. My ear is not good enough to distinguish the tonal difference between a 330/12 and a 360/12. But any way you go, you'll get that Fabulous Rick 12 Sound!
PS: Despite what I said about playing out with a 381, a gentleman with the handle of bobfoleywines has a thread on the "Ricks for Sale" topic on this forum where he sought help in locating a replacement for his damaged 381V69 6 string that he gigs with. You could contact him and get his take on why he prefers a 381. Plus that thread provides some info on where 381s may be available.
PPS: Here's one just up on ebay, beautiful flame maple, min bid $2800:
http://cgi.ebay.com/99-Rickenbacker-381 ... dZViewItem
Good luck and happy hunting.