Just looking at the schematic of the pre-amp, the two do look mighty similar. The biggest differences center on what has been added, not necessarily what has been changed. If you've ever done any amp building or amp modification, you'll know that hanging more components off a nominally-identical circuit produces changes in the sound. So, additions are just as relevant as changes.
In the Mark IV, some sizable additions include:
1) All of the components used to implement the extra tone knobs (for R2 and for LD)
2) All the components to implement R2
After these additions, some sizable changes include:
3) The volume controls (R1 Master, R2 master, and LD master, output level) are implemented somewhat differently, especially for R1.
4) The effects loop is implemented quite differently
5) There is no "Pull Deep" switch, though the IV basically has the same circuit elements wired permanently "On"
6) The gain stages in the lead circuit, while being the same number in both amps, are implemented in different tubes in the two amps. In the IV, both gain stages are implemented in V3. In the IIC+, though, one stage is implemented using half of V3 and the other stage is implemented using half of V4. There is debate as to whether that's relevant. What is clear, though, is that while the schematic for two lead circuits might be the same, the physical circuit paths are different because of the need to route the signals around to the different tubes.
Generalizing from this last point...what you can't see in the schematics are the differences in the physical layout of the circuit traces throughout the twp amps. The circuit boards for the IIC+, the III, and the IV are all different from one another. The physical layout of the traces matters. For those who are familiar with the issues of "lead dress" in old point-to-point wired tube amps, the removal (or addition) of a few inches of wire can make a surprising difference (usually in how it picks up or avoids picking up "ghosting" and other types of overtones or intermodulation due to capacitive coupling). Changes in the traces on a circuit board are just like changes in the lead dress...it can make a big difference.
Along similar lines, the schematic also doesn't show what specific kind of resistors and capacitors are used or what their tolerances are. While I myself am skeptical about the impact of different resistors, I do believe that the type of caps can make a difference. Now let's be clear...I'm not talking about differences in the supposed "quality" of the caps like often touted by the Hi-Fi audio snobs...no, no...I'm just talking about the impact of the basic choice of cap type (cermaic vs mica, poly-pro vs poly-ethyl vs poly-styrene, etc). The different cap types have different types of non-ideal behavior inherent in them...difference levels of series resistance. inductance, DC leakage, microphonics, non-linear behavior at high voltages, etc. So, if you swap enough caps in the amp from one type to another (as happened during the ~10 years between the IIC+ and the IVB), you will likely hear and feel a difference.
So, if you're really curious to track down why the two types of amps might sound different, you might need step beyond the schematic and find some gut shot photos. Take a look at the paths of the circuit traces and what caps are used.
Chip