Modelling amps are mostly built to take a guitar input.
The thing about boosters and overdrives and some distortion boxes, they push the signal above what is a usual guitar signal. In simple way you can say your guitar usually provides -5 to +5 Volts. These effects push it to -15 to +15 Volts. This is just an anology of course, it doesn't really happen like this.
Now, with a tube amp, tubes take high gain signals very nicely. The tone compresses evenly and warmly, giving people the overdriven tones they love.
With a normal solid state amp, the transistors don't like the higher gain signals too much, but they can work with them. Usually they tend to be a bit fuzzy sounding. Some designers however have been able to replicate tube like responses using transistors.
With a modelling amp, you have a big problem. Myself I do not know exactly how they process the signals. But in my opinion they like to work on a simple guitar signal and process it with their own effects and models. If you give it a strange (higher gain) signal, it gets confused and you get sounds that you may not want.
Ciel's Toadworks Death Rattle II sounds great through his tube Laney and not too bad through my SS Trace Elliot. But just the other day we played this gig and he played through this Crate modelling amp. It farted when he kicked in the distortion. Let me repeat that.
It farted.
It went PRRRBBBRBRBBB!! PRRBRBRB!! PRR-PRR-PRR-PRRRBRBRBRBR!!
I was laughing my ass off.