Of course, private wallets have better advantages at the moment, because perhaps this is my personal opinion, that the private key that we control sounds more secure than entrusting the private key to someone else (exchanger). However, this also depends on our goal of saving money, whether we want to hold it for a long time, or just focus on daily trading. Considering that blockchain networks always require transaction fees, and bitcoin transaction fees are quite fluctuating, so choosing a wallet really depends on conditions and needs.