1. Hacking
2. Limiting Account
Unlike bitcoin core, you don't have any control over coinbase or the same types of wallet. Coinbase, in general, is an exchange and a wallet for the newbie who get trapped by them by google.
Limiting account means don't have control over funds right,but this is good thing for the newbie who don't know what fee need to use for transacting so they get end up setting default fee from coinbase but newbies need to learn quickly about crypto wallets rather than trusting online wallets for long time.
Its clear that which one is better hence, coinbase is an exchange and majority does know that if you store up funds on an exchange wallet which
you dont own the keys then you simply dont own those coins completely when you store it up there.
But bitcoin core or the wallets which gives private keys are the best still might have complications for the new users.