I appreciate the feedback everyone left on this subject. I've been digging into the specs and reading the various guides, but none of that can compare to your experiences.

I've learned:
1) Most folks prefer the 337. Faster, sexier, newer, neater, line-boys don't snub you as often, etc. ;-)
2) The 336 will cruise at about 140 kts - about 15 kts slower than a 337.
3) Vibration may be more of an issue in the 336.
4) 337 has better cooling (scoop, no fan), but 336 owners don't think it's a problem if baffles are OK.
5) 336 owners seem very happy with their airplanes.

I put the insurance question out to the nice lady that takes my money and I'll let you know what I find out. I'm a relatively low-time pilot with most of my time in a 182.

Bob