What’s the difference between a Passphrase and a Private Key? Which is more important?
They are closely related.
Private Keys: At the level of the actual blockchain, what matters is the private key for the given wallet address. All you need is the private key to send funds out of the wallet address.
Private keys give control over funds.
Passphrases: The passphrase exists at the level of the wallet app. The passphrase is used to seed the system that generates the wallet address/private key, but the passphrase is much more human-friendly than the private key. One can’t use the passphrase to do anything on the blockchain - but once can use the passphrase to re-create the address/private key, and then one can send funds out of the address.
Passphrases lead to private keys, which give control over funds.
Result: either one gives access to your coins.
Multi-coin note: multi-coin wallet apps will generally have one passphrase which seeds the system to generate the wallet addresses/private keys for all the wallets in the app. So someone who gets the passphrase can re-create the addresses/private keys of all the wallets and gain access to all of them.
Passphrases for multi-coin apps lead to private keys for many wallets, giving control over all of them.
So… what takes precedence?
They are all critical and should be handled with a high level of care.
If you must rank priority, I would not base my thinking on key or phrase: I’d base it on the value stored in the wallets! The more value, the more careful.
Common practice: keep some funds in multi-coin wallet apps on a mobile device for convenient usage, but keep most funds in a different wallet/different app which is not accessible from the mobile for safe keeping.