I believe when two light meters disagree it's most likely one of a few factors. Analog light meters can easily get out of calibration because of the delicate needle balance. The motion picture Spectra meter was the standard, but if you look at it wrong, it would need recalibrating. Older meters have older photo cells and older technology. But mostly, I believe it's do to the spectral sensitivity of the photo cell.
The basic values in the exposure equation haven't changed since they were established in the early forties and except for a small change as the result of better measuring devices, is the same from the point of the first ASA standard for exposure meters sometime around 1948. The changes in the standards over the years seem to be mostly attributed to the changes in the materials that make up the photo cells.
I remember reading something from the late 50s or early 60s about a change in the kevin value used to calibrate the meter. It was to change from something around 2700K to the cooler 4700K used today. At that time, films tended to have a different EI for daylight and incandescent light. I believe it wasn't because of the emulsion, but because of the spectral sensitivity of the light meter and the color temperature of the calibrating light source. If I remember correctly, the paper said that after the adoption of the proposed change to a cooler calibration light source, there would be no further need for two film speed ratings for each film. According to the paper the goal was to "make more accurate in daylight and eliminate the need of different tungsten speeds for most panchromatic materials." And by the mid or late 60s, I believe this was the case.
So when comparing an older light meter with a newer one, even discounting the affects of age, the older meter might have a different photo cell that responds differently to the same color temperature in addition to being calibrated to a different light source which under under certain circumstances could combine to make quite a difference.
If anyone wonders if the sensitivity of the photo cell makes much of a difference, there's the infrared test. A quick test to see if your meter is sensitive to infrared is to point it at a remote. Meter the remote, then push a button on the remote and see if the meter reacts. If it does, then it's sensitive to infrared. Many people tend to use foliage like grass to key off of. As anyone who has shot infrared knows, chlorophyll reflects tons of infrared. A meter sensitive to infrared will see the grass as brighter than it really is which may cause underexposure.