Actually, Carver showed that an amp could be *modeled*, but even in his tests the modeling did not match the actual behavior of a tube amp.
Mapman, here are some primary differences.
1) Tubes are often much more linear than transistors. Triodes are the most linear form of amplification known. This results in far less need or no need at all for feedback to reduce distortion.
2) tubes produce mainly lower-ordered harmonics, transistors tend to produce higher ordered harmonics, especially odd-ordered. This can be easily seen in the overload characteristics of the amplifiers where these behaviors are exaggerated. Anyone who has run an amplifier into clipping and observed the output with an oscilloscope knows what I am talking about
3) tubes tend to high impedance while transistors tend to low impedance. In addition, there are capacitive effects in transistors that are magnified at higher currents. The effect of this is that both transistors and tubes will sound better (lower distortion, smoother sound, greater transparency) when driving higher impedances.