There are lots of differences between the two services.
- A self hosted service runs on your current internet connection therefore the only price you pay is your ISP bill while an online web hosting account will cost a yearly fee depending on the provider.
- On your self hosted service you are not bound by the limitations imposed by the web hosting provider eg, data space, number of email addresses/accounts, control over server settings, number of domains hosted, scripting, databases & extensions, site management tools.
- On an online webhosting account your privacy is always ignored as someone always checks on your stored data while on a self hosted service you control permissions on whom accesses what.
- Email privacy is always a concern specially when the mail server is provided by an online service provider, while a self hosted service is controlled by you and data is all on your own server.
- On a online hosting account the data is usually backed up by the provider while on a self hosted service you control the frequency of your backups.