Why?
1. Component accuracy and drift.
The components used in tube amps are low-cost, consumer-grade parts. They typically have tolerances of 10% or more. Over time the value of these components drifts. If your amp is old chances are it doesn't sound like it did when it was new. All our old reference amps are given a thorough checkup prior to modeling with any out-of-tolerance parts replaced.
2. Potentiometer tolerance.
A typical consumer potentiometer has a tolerance of up to +/- 20%. That's huge and that's end-to-end accuracy. On top of that the midpoint accuracy can be another +/- 20%. So if you have a 1M pot it could be as low as 800K. If it's linear it's midpoint should be 400K but could be as low as 360K. Now your 1M pot that should be 500K at halfway is only 360K. That's an error of 28%!
3. Potentiometer taper.
A big one. Potentiometers come in a variety of tapers: linear, 30A, 20A, 10A, etc. The taper on an audio taper pot (i.e. 30A) denotes the value of the pot at mid rotation. For example a 1M, 10A pot would be 10% of its value at "noon", or 100K.
Manufacturers are constantly changing the taper of the pots in their amps. Sometimes the designer changes the taper as customers are reticent to turn knobs much away from noon. It's a weird psychological thing. Sometimes the manufacturer changes the taper due to availability concerns. Sometimes they change the taper when moving manufacturing locations. Sometimes they change the taper for no apparent reason at all.
Another factor is that almost all amps don't use true log taper pots. They use "commercial log" taper which is a crude approximation to a log taper. This is because true log taper pots are expensive. Fractal Audio products use true log taper. This means that '7' on your amp is not exactly '7' on the model even if the pot in your amp is exactly 1M and its taper is exactly 10A. Why do we do it this way? Because the response is smoother and if true log pots were the same price as consumer log pots everyone would use true log taper.
We model all amps assuming the pots are ideal. We assume the end-to-end resistance is exactly, say, 1M and the midpoint is, say, exactly 100K. We DO NOT use the values measured in our reference amp because no two amps are the same so we use the DESIGNERS INTENDED VALUE.
What all this means is '3' on your amp is not necessarily the same as '3' on the Axe-Fx.
Example: the Master Volume pot in a 5150 is a 1M, 15A audio taper pot. Theoretically it should be 150K at noon. On our reference amp it's about 15% low. If the reference amp's MV is set to '3' we have to set the model to around '2.5' to match. This is unsurprising due to the tolerance of the reference amp's pot.
4. Indicator accuracy.
On many amps if you set a knob to noon it's not actually halfway in the pot's rotation. Why? Several reasons. Some amps are just weird. For example the Bogner Shiva's minimum rotation is around 6:00 and the maximum is around 4:00. So noon is actually past midpoint. Same with Soldanos. In other cases the knobs aren't oriented perfectly on the shaft. If it's a knurled shaft the knob may be off one tooth. If it's a smooth shaft then you're at the mercy of the human who put the knob on the shaft and tightened the set screw. This is why I prefer D-shafts. Finally the pot itself may be rotated relative to the panel.
You can try this yourself. Turn the knob on your amp fully CCW. Note the position of the indicator. Now rotate fully CW. Note the marker position. If it's an old amp it's probably not symmetrical.
Then there's the whole marking thing. Fender's are numbered 1-10. Soldanos go to 11. We use 0-10 so be wary of the amp's numbering.
5. Power Tube Bias.
Another big one. The transconductance (gain) of a power tube can vary greatly. This is why power tubes are color coded, sold in matched sets, etc.
Amps come in two flavors: fixed bias and cathode bias. Fixed bias amps apply a "fixed" voltage to the grid of the power tubes. Cathode bias amps use a resistor between the cathode and ground to self bias the tube.
Most, but not all, fixed bias amps allow the user to adjust the bias point of the amp. This allows the bias point to be set to an optimum value for the particular set of tubes installed (since the transconductance can vary greatly). Some fixed bias amps do not allow adjustment. Examples are Mesa/Boogies, 5150s, and several other brands/types. The drawback of this is that the bias can vary greatly depending upon the gain of the tubes installed. Due to this the manufacturers err on the safe side and the bias is usually much colder than the ideal value.
Most cathode biased amps are not adjustable. Again you are at the mercy of the tube's gain but these amps tend to be biased hot to begin with and have higher transformer matching which prevents excursion outside of the S.O.A. (safe operating area).
If the bias is adjustable where the manufacturer decides to bias their tubes is a matter of preference. Most manufacturers bias their tubes on the cold side to prevent premature failure and reduce warranty claims. Especially the larger manufacturers.
This leads to the question of "what is the ideal bias point?" The pervasive school of thought is you adjust the bias so the idle dissipation is 60-70% of the tube's peak power rating. This is a safe approach and ensures that the tubes don't "red plate" and live fairly long and prosperous lives.
My opinion is that the ideal bias point is NOT a function of the tube's power rating. It's the point at which the power amp's transfer function is most linear. Unfortunately operating the tubes at that point can result in exceeding the tube's S.O.A. So the optimum bias point depends on the tube's power rating, the transformer primary impedance (matching) and the user's tolerance to tube replacement frequency.
For example, if we bias an EL34 based power amp at 60% peak dissipation it's actually running fairly cold. If we know that the transformer is slightly overmatched we can bias the tubes hotter, 70% or even more. This will result in a warmer tone but the tubes will wear faster.
What does all this mean? Well, I bias the virtual tubes on the warm side. EL34s are biased at around 70% because we don't have to worry about them wearing out. 6L6s are biased a little colder, around 60% but this is actually as "warm" as the EL34s because of the higher plate dissipation of a 6L6.
In practice this means that the models in the Axe-Fx will biased warmer than a new amp straight out of the box as most amps are biased cold (too cold IMO). After you wear the tubes out and bring it to a tech the tech will replace those tubes and bias them hotter than factory. So if you're comparing your new, out-of-the box 5150 with the Axe-Fx model the amp will probably sound "colder". Some people like this, many do not. If you like a colder sounding power amp it's just a knob
The models in our products are based on our in-house reference amps. If a model doesn't sound like your version of that amp it won't sound like our reference
