offline cold is always safer then online exchange or wallet. When you hold large amounts of Bitcoin or other cryptocurrencies, you should go for a hardware wallet instead of using a software wallet. Because the hardware wallet will always be offline so in this case hackers will not be able to hack your crypto. Online non custodial wallets are also unhackable if you keep your private key secure. In this case, keeping a note of the private key offline is much safer.
Cold storage, offline, airgap, is best storage method, better than storing your bitcoin online in hot wallets. Exchange accounts are one of worst ways to store your bitcoin because first it is a hot wallet, and second but more important, it's not your private key, it's not your bitcoin. Exchanges own private keys of customer wallets, while customers don't own any private key.
Reminder: do not keep your money in online accounts