The so called "memory effect" in NiCad batteries is largely a myth
the MAIN source of pain in rechargeable batteries is the discharge rate. Remember, a battery is generating energy by letting a chemical reaction occur bwetween two ionized components. This invariably results in crystal growth
The faster you let the battery discharge, the faster the resultant crystal growth. And if you remember playing with Rock Candy as a kid, the faster the crystals grew, the larger they were.
Unfortunately, the larger a crystal is, the more stable a bonding structure it is. Which means that if you discharge at a rate above the "ideal rate" for a particular battery, you will grow crystals that are large enough that you cannot re-dissolve them at normal charging levels. Shipboard systems for example provide an Overcharge rate to deal with this in Lead Acid batteries, but you can't do the same thing with a cell phone or similar device.
So what does this have to do with your old Sony phone? Well the older phones OVER Specced the battery capacity. Furthermore as a household phone, the marketing perception was that you wanted to give a more "solid hand feel" to the customer - which means a bigger battery - which also means more talk time.
OTOH, newer phones started going down the "cell phone" path - by UNDERSPECING battery capacity and essentially over-discharging the batteries - thereby shortening their lifecycle by the creation of the above oversized crystals.