Both have their advantages and disadvantages. It would just really be on your personal preference to choose which one will suit what you want and need.
Exchange Advantages:
1. Convenience - It is convenient to use in a sense that you don't have to undergo many and long processes before transacting. This is easy to install as well and most of the time free download in PlayStore or AppStore. After you download, you'll just follow a few steps to be able to make and use your account. You can access it anytime, anywhere as long as you have your gadget in you, you can open your account.
2. Easy to learn how to use - Because of its simple interface, it is easy to familiarize and to use regardless of age bracket. Its features are mostly comprehended quickly as well as the runaround inside the exchanger platform.
Exchanger Disadvantages:
1. KYC is required - To some this is a disadvantage that's why I put it here. In most exchanges, KYC is mandatory most especially if it is a centralized one because they just follow local government protocol as well as to detect the accounts of those people who are doing illegal activities such as laundering money using their platform. This possess a risk because once you give your consent in providing your personal information to them, they could use or sell it without you knowing, despite having the agreement that they will keep your personal data private. Unfortunately, this really happens. In addition, identity theft is also possible once their security has been breached which could lead to a bigger problem in the future if ever it happens.
2. Hacking incident is frequent - I think most of us are already aware of this. Several incidents have been reported in the past up until the present regarding this issue. Exchangers, most especially the centralized ones are prone to hacking because they have weaker security protocols compared to others which is the reason why it is mostly infiltrated by hackers. Recently, coinbase has been compromised which just caused thousands of users to lose money they have their account. Despite the OTP feature and other security measures of exchangers, the hackers still manage to bypass the security with just a few clicks and viola! they were able to stole huge sum of money that cannot be returned back to the account holders.
Hardwallet Advantages:
1. Security - No doubt, hardwallet is really the best when it comes to security. If you want your assets to be safe, it is recommended to have a hardwallet that could gatekeep your assets while you are doing your own thing. Because hardwallets have a built-in and specialized chips in them, it is harder for a hacker to infiltrate your account. Once they try, they won't be able to succeed unless you give your password and seed phrase to them wide open.
2. More coins are available and many accounts can be stored - In hardwallets, there are more options in coins. You are not limited to the usual coins but can access many coins in which you can invest and trade in. In addition, you could add more accounts depending on your hardwallet model. In some hardwallets, it has 20 maximum accounts, some 50 accounts, and so on. Of course, this varies in accordance to the price. Indeed, you get what you pay for.
Hardwallet Disadvantage:
1. Cost - Hardwallets are expensive. Most of it costs over hundred or even thousand dollars depending on the brand, model, and features. But this should not be viewed as a worthless expense because we are talking about security here. If you can afford to invest in crypto, you should also invest in security. Because once your account has been hacked, all of your assets will be compromised, be gone, and all put into waste in no time.
I hope I was able to answer your question and help you decide which one is better by laying down all the information about the two.