Back in the day when these two speakers were new, the conventional description of the principal difference between the two speakers was that the Vandersteens were darker in overall tonal balance (slightly tilted to the bass regions) and the Thiels were brighter in overall tonal balance (tilted more to the treble). While I liked them both and heard them both extensively, my preference at the time was the Thiels, and I tried an Aragon 2004 amp with my Thiel CS3s with good success (though I ultimately got a Krell KSA 50 instead). Both use first order crossovers, and both are well-designed. The Vandersteens sounded good with both an inexpensive Rotel amp and, while a little lush, with Quicksilver monos.
Your room size might matter; generally you should sit at least a few meters away from the Thiels to get optimal blending of their drivers. The Vandersteens were set up and sounded good in a small room (at Audio Connection, before Johnny R bought the business).
I have not heard the Von Schweikert bookshelves, but if they're like the VR 4s (which I have heard) I don't know if this would be a move forward in sound quality; maybe more a lateral move, IMHO. The Thiels go down to 40 Hz and drop off quickly after that (which is why I got the CS3 demos instead of the CS2s), so your setup with the sub might go lower. Is there something about your current setup that you'd like to improve on?