I don't think Electrum is particular private either. In both cases you are connecting to a server ran by a third party who can then see all the addresses you are querying and all the transactions you are broadcasting and then link them altogether.

Ledger will be worse in some aspects, since they can potentially link your address data to some other personally identifying information about you that they store, and they will be able to link all your altcoin addresses too.

Electrum will be worse in some aspects, since you are connecting to many different servers which increases the risk of connecting to a malicious one who is spying on you.

The upside to Electrum of course is that you can point it at your own server (or a specific server ran by someone you trust).