The 606 just ticks all the right boxes for me, looks great, sure - they are expensive - but not as insane priced as some other high end brands, room friendly can be up close to a wall if need be, powerful but refined sound etc , etc.
I can’t speak directly for S10s (though my familiarity with them goes right back to the prototype pair up to the active-capable production model), but I’ve owned C10s since 2008, in the two different iterations: MDF cabinets with jumpers, and HDF cabinets with single wire inputs. I prefer C10s to C20s, for the reason you state. For me the 10 is a more integrated sound across the frequency spectrum. Darned fine speakers.
Both Naim and Chord Ultima amps will bring the best out of Titan 606 speakers. I have heard both combinations and currently own Chord Ultima in the main system but Naim for the other music systems.
I’ve heard the Ultima 5 drive 505, 606 and Titan 808 speakers with effortless ease. The Ultima 6 will drive the 606 well too, as will a Naim New Classic 250 or the NAP300 which was used by Kudos during the development of the 606.
A demonstration at a decent dealer is probably the way to go at this point.