If my goal is primarily to sample records from a tape deck or record player, which one of these add on a would be more beneficial?

For your purpose, neither the mLAN16E or AIEB2 would be necessary or perhaps even desirable.

Presuming the tape deck and turntable were connected to a stereo preamp or receiver having a “tape out” connection, that output would be at line level. Such a signal could be directly connected (with proper cables) to the A/D INPUTs of the ES, with “Line/Mic” in Utility mode set to “line”. The ES end of the cables should have TS type 1/4” phone plugs.

Connected that way, it would even be possible to apply Insert Effects to the incoming signal, if desired. That can’t be done via mLAN or AIEB2.

If there’s a reason the above wouldn’t be acceptable, please provide further details.

No that entirely answers the question. Thanks