Is it safer to keep coins on an exchange or in a wallet?

It depends on the amount and purpose:

• Exchanges: Convenient for trading, but essentially the platform "holds" your assets. Suitable for small amounts or frequent trading, but be sure to enable 2FA, anti-phishing codes, and withdrawal whitelists.
• Self-custodial wallets / Hardware cold wallets: You control the private keys yourself, better suited for large amounts or long-term holding. The trade-off is that you must safely store your seed phrase — if lost, no one can recover it.

In short: Small amounts on exchanges, large amounts on cold wallets, balancing convenience and security. For wallet differences, see What is a crypto wallet.