....Having an amp with the distortion set low for cleans then using a TS to distort it or having an amp cranked so it is overdriving quite a bit and using the volume to clean it up?
Depends on what you want. The first will work the best if you want to go from clean to lightly ODed tones. The second will work better if you want to switch between cleans and more heavily distorted tones.
Personally I like cranking the amp and cleaning it up.