As an "old fogy" from BA central area, you probably wouldn't notice that much difference in the logs from when you retired [apart from on the very new aircraft, I'll go back to that later].
The main differences from when you were around, is that the logs have gone from a "landscape" format to "portrait" This happened a number of years back in BA, the new format also saw the transfer of all the log data onto the "SAP" computer system which keeps a tab on all the ADDs, repeat inspections etc so in theory you shouldn't get an overrun. That does depend, however, on accurate information being entered by the engineer to start with in the log and the person transcribing the info into the computer system. Also now, what was the Cabin Log has become the Aircraft Log Part II and is in the same format as the main [Part I] log with the same legal standing. Oils and Fluid uplifts are still entered manually into the logs although I think the SAP system takes care of the flying hours. Logs also contain details of current software, damage charts, lists of mods etc, all the same as in your day.
So still, two pretty hefty logs.
The new generation aircraft [B787 and A380] are an entirely different beast though. They have "e-logs" as as you might expect the defect/information is entered by the crew [or an engineer] via either the touch screen [crew] or by a maintenance laptop or the touch screen [engineer]. The entries also being "signed off" electronically by the engineer after fixing [or deferring] the defect by entering his licence number and his password.
The e-log will then upload the information via various systems so that the information goes straight into the mainframe computer system on the ground, so the information no longer has to be entered into the SAP computer system manually.
Also when entering in a deferred defect you are prompted to put in parts required and that demand then goes into the system [the bits are still nil stock though, just as in your day
]
This is a pretty good concept but there are still quite a number of "old fogys" [you would probably still recognise a lot of people at BA!!] around and with many of them data entry via either a keyboard or a touch screen is probably slower than filling in a traditional style Tech log