I've heard something about electrum having their own servers the electrum wallet talks to instead of directly to nodes or whatever that other wallets talk to and that this has some theoretical privacy implications. Is this true?
If you connect to a random (i.e. not your own) electrum server, yes.
The electrum server you are connecting to has access to the following information:
- All addresses which you query the balance for (every used + every address in your 'receiving address' tab)
- All transactions you send
- All transactions you receive
- Your overall amount of BTC
- The time of the day when you send / receive a transaction
- Your IP
Note that every wallet (which is not a full node client) can gather these information.
The only way to circumvent this is to either (1) run your own electrum server or (2) use a different (full node) wallet, e.g. bitcoin core.
Is this better or worse than any other wallet?
It is definitely not worse than other (desktop- / lightweight-) wallets.
It even can be regarded as better because you can choose to which server you want to connect. You don't have that option with the majority of other lightweight wallets.