I vaguely remember a paper which stated that in their current implementation, lightning watchtowers require a lot of memory because they need to store information about (a penalty TX for) every balance change that happens on a channel they watch. And that eltoo would be more memory-efficient because it only requires storing information pertaining to the latest respective state. However, when talking about this in a large group of bitcoiners, there was no consensus about this. Does anyone know whether this is actually the case? Does a watchtower really need to store info about every channel balance change?
Without eltoo (ie today) a watchtower needs to store a different justice transaction for every channel update in case the channel counterparty broadcasts (deliberately or accidentally) an expired channel state.
With eltoo (once/if we have SIGHASH_ANYPREVOUT enabled onchain) a watchtower will only need to store a single justice transaction in case the channel counterparty broadcasts an expired channel state. The watchtower can delete old justice transactions.
This presentation from Christian Decker at Chaincode Labs is a great resource on eltoo.