"Sounds digital" is a critique of modelers I've seen a lot, but it's something that has never really meant anything to me. It's probably a side effect of my history with equipment and playing, though -- there was an old 30W Yamaha solid state combo amp I played through growing up, but never with the volume higher than probably 1 or 2, then I had an overpriced 15W Crate practice amp, then a Behringer V-Amp2, and now the HD500 and Guitar Rig 5/Amplitube 3 VSTs. I also hear people say things about how a model might respond like a real amp in the sense of cleaning up when you roll off the volume or pick attack, but I'd been playing at least 15 years before I ever saw anybody adjust their pickups, volume knob, or tone knob while playing, so... maybe I just don't notice that sort of auditory nuance ;)
It's been a while since I messed with my POD or tried to create any patches, because I stopped playing out much and so I mostly just record with Guitar Rig right now. But yeah, my recollection is that either my distorted rhythm patches would sound wimpy because I would turn the channel volume down and master up, or my clean patch would distort because I would have to bring up the gain.