According to the specs, there also appears to be a difference in discharge curve charachteristics between the two cells. In my experience, this diffference has been negligible effect, if anything.
The difference between 1.35V and 1.5V is about 11%. While is does not necessarily follow that meters will thus be off only 11% (it depends on the design of the meter), my experience is that the significance of this difference is usually an overstated worry. Within the limits of the linearity of the meter at the ends of its measurement range, you can dial in a lower EI to overcome the tendency of a meter to underexpose when running with the higher voltage.
The greater concern is that the only batteries made today that will physically fit in the old PX625 form factor are alkaline. Alkaline batteries have a well known problem of gradually losing voltage over time and this gradually introducing measurement error with meters. The better solution here is to use silver oxide or lithium batteries, none of which are made in that form factor any longer. The silver oxide and lithium batteries maintain their voltage until end of life and then fail very rapidly.
So, if you have meter that still expects a 1.35V battery, you need a voltage dropping device like a true MR-9 with a silver oxide battery installed.
If you've had the meter re-calibrated for 1.5V, you need a physical adapter without a voltage dropping diode just to be able to use the smaller SR43 or SR44 batteries. As has been pointed out upthread, these can sometimes stand "proud" of the battery compartment and make threading in the cover difficult. Some people have reported good results by using o-rings to hold the smaller batteries in place in the larger 625 battery compartments.
I was fortunate to squirrel away some S625 batteries when they were still being made. I use this with my re-calibrated M5. When they are gone, I will have find an SR43/44 solution that works.
