If it's a really large amount of money, I would prefer to put it in cold wallets compared to the exchange because you have more full control over your assets, while in the exchange you don't. Because the risk in the exchange, especially if it is centralized, is that it can shut down anytime, and when that happens, you have no choice but to wait, just like what happened with Ftx.

But if in the cold wallet way there is nothing like that, instead you really have control over your assets and there is no KYC that needs to be given, but it depends on the trust you give to the exchange or how reputable it is, like Binance, Bitget, and Bybit. In short, do it at your own risk.