Online wallets offer greater convenience. You can generally access your Bitcoin from any device if you have the right passwords. All are easy to set up. The disadvantage is the lower security. With your private keys stored in the cloud, you have to trust the host's security measures.
Hardware wallets are small devices that occasionally connect to the web to enact bitcoin transactions. They are extremely secure, as they are usually offline and therefore not hackable. However, they can be stolen or lost. Some large investors keep their hardware wallets in secure locations such as bank vaults.