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.
Basic thing and theres no need to repeat this kind of illustration yet there are lots of topic already towards this matter. Exchange wallets would only give advantage if you do make active trades but if you do tend to hold for long term then hardware wallets would be suggested. Storage will be depending on ones decision on where which path hes going either for long or short term.As long you are aware into your own coins then it should be fine.