Vandy 2 or 3 Sig. Vs. Thiel CS2.2 or CS3.6 or ??

It is a matter of personal preference, but my choice would be (and in fact, is) the Thiel CS3.6. However, 3.6's are rather hard to drive. They are 4 ohm nominal, but spend a lot of time in the 2 ohm region. I don't know a lot about your amp, but you may want to see how well it handles difficult loads. If you push them right, though, 3.6's will perform as well as the rest of your gear will let them.

These two speakers have quite different tonalities, so it's hard to directly compare them. If you are not familiar with both, you should do some auditioning before you make a purchase. Tombowlus' comments above are also correct, so you should try to audition the speakers using the same amp if possible.

Sdcampbell offers good advice. These two speakers are about as different in their characters as it is possible for two dynamic driver speakers to be. Which you will prefer will depend on your listening priorities. Audition definitely required. The Vandersteens are an easier load for most amplifiers and will mate very well with most tube amps (particularly the Vandersteen 2s), the load presented by the Thiels will be more challenging.

I concur 100% w/ sdcampbell. Very different speakers. To over-simplify, vandy's have a warmer richer sound, with the thiels being tighter (in the bass) and more cyrstalline (in the treble). FWIW, I've been a very happy vandy 2ce owner for about 3 years now. Hard to beat in their price range (used), though it sounds like you have a bit more cash to play with.

I also Agree with SD Campbell and Shersta
with the one exception that the Vandersteen will deliver better in room bass as the Vandys design shines well with room nodes. The front 8 and rear 10 spreads the bass payload in 2 parts of the room which leads to less agitation. Try the bassline on Allman Bros Statesboro Blues on this one.
Cheers Johnnyr