GhostofCain
Ancient Mariner
You've answered your own question.
The drum sound on LAD is called "cardboard drums". Caused by the recording technology and crappy practices of the day. Noone wanted that sort of a drum sound, but they couldn't do better.
LAD is judged in the context of its time. Drums don't sound good but the playing is excellent and since that "not good" is the standard of the day, it gets a free pass. However it's 2020 and we have 30+ years of sound development.
What LAD does great, is the guitar sound that complements the drum sound. Guitars are thin too, but razor sharp, energetic, and full of clarity. It makes the whole recording very 'airy' which is not an usual feat of a live metal album (wall of sound ftw amirite). This is achievable cause one of the best bassists to ever grace the rock genre glues the drum and guitars together. All ads up to unique character of LAD and why it's considered as greatest of all time type album.
LAD drums weren't wanted, but they got them and needed to work around it - hence the other production choices.
None of this is present on the current live release, Harris's bass plays a different role in the last 20 years due to the 3 guitar setup, it's quite impossible to create a perfect clarity of 4 heavily distorted electric string instruments in a stereo space.
Two words explain how good Live After Death sounds: Martin Birch. The guy was a genius making things sound heavy yet incredibly clear at the same time.