what do you use wallet or exchange for? Do you want to trade or hold ?
If you hold on a mid term or trade, you should use exchange. And hold your coin for security, you should use hardware wallet.
Wallet without fail... if the exchange gets shut down game over you loose out.
You must also consider trading patterns. If you are an intrа-day trader no way you can move your coins every hour between wallet and exchange. But, if you plan to hold a coin for long time, not use it in your intrа-day, then store it in a cold wallet.