i usually attribute that quite a bit to the guitar / pickups than just the amp, my favourite guitar for that has been my kauffmann telecaster, super low output pickups, running into the matchless preset above , with a bit of boost to up the pickup signal going into the amp, works wonders
i've linked a video i did just for the first part , to give some idea
the touch sensitive part i usually get the most out of it with an edge of breakup style sound, roll the volume knob back a bit, or play with a lighter touch
as an example Andy Timmons i think has a Keeley modded Boss Blues driver, that's pretty gained up, and he rolls back the volume (with a treble bleed on it ) works wonders i think
as others have said gain/volume will play a big part, i like clean boosts or even using the Blues Driver model in the drive block to add some grit/personality, to amps that might be 'too' clean , hope that makes sense
in terms of amps, i really like the Matchbox D-30 , ODS, even the plexi style amps with your volume knob rolled back is great