The only increase in accuracy is along (or very close to) your meridian. The azimuthal equidistant portion (blue curve) slides radially along your meridian from the pole. Thus, your elevation will be more accurate.
The issue is that the AE curves gradually change shape as latitude changes. Pull out your red overlay for the 2102D. That actually is the AE curve for 90° of latitude. Perfectly concentric circles. The circles are slightly deformed for the 85° AE curve. Now examine the AE curve for 5°. The circles are enormously deformed. The point of this description is that the AE curve has a unique shape for any unique latitude. Simply sliding a curve generated for 45° to 40° does not make it a 40° curve. The shape is wrong for that latitude. Therefore, the resultant altitude and azimuth will not be corrected when using the 45° AE curve at 40°.
Here is an example to mull over. I set both the 2102D and the CP-300/U to LHA Aries = 0, using the 45° AE curve. The altitude and azimuth for Altair are 25° and 257° for both instruments. Suppose now we are at N40°. The 2102D result does not change. The CP-300/U permits us to slide the AE curve. This now provides us with 24° altitude and 260° azimuth. I went to the USNO and obtained Hc and Zn for Altair, they are 26.88° and 258.5° respectively (19 March 2008 12 hr 10 min 11 sec and AP is N40° W0°).
The CP-300/U changed the result when we adjusted the AE curve, but it did NOT provide more correct results, merely different results. If the AE curve was adjusted in shape to account for N40° the results would have improved. This was the purpose of my 2102E, in the archives.
You correctly ask, does any of this matter? The main purpose in the 2102D is planning. "At twilight, I will observe these bright stars" or "I saw a very bright star, which one was it". These activities do not require oodles of precision. Either device will provide sufficient results.
In my opinion (and it is just that Alan, an opinion, yours may differ), sliding the AE curve on the base provides little benefit. I consider it a feel good exercise, that you somehow have gotten better results from the device. As we have seen from the example, they may not be better, just different.
The smaller scale of the CP-300/U is a drawback. The AE curves are smaller and harder to read. As Gary has pointed out in the past, it does offer negative Hc, when flying at high altitude, so perhaps there is a small advantage there.
PS Perhaps you would like to test the accuracy of both devices for Alioth, Dubhe and Kochab. You should note an increase in accuracy, as these stars are close to your meridian.