In my limited experience(and I haven't tried the expensive stuff like Kemper or Neural dsp), the difference is most apparent to the player in the way amp and effects react to playing dynamics. For a blues player sat 'on the edge of overdrive' the effect of injecting emotion into ones playing comes through the amp in a way I couldn't get with a digital amp. This the affects the players response. I feel like a million dollars through my Fender Twin. I close my eyes and channel my Stevie Ray. It didn't happen to me through a Boss Katana. If you were paying to listen to me (as if), you would get better vfm from the tube amp.

If I played metal, or was backing a pop group, one pedal di'd to the desk sounds like the dream