Odoo Online is limited and not licence free option given by Odoo Enterprise the biggest disadvantage of Odoo Online is startup cost as well as potential problems in the future. We have seen many businesses started with Odoo Online and after few Months they would like to switch to Odoo Community Edition because the licence cost was $500/Month + They cannot install any Application since its "As-Is" means you are not allowed to install any application into it.(Imagine this like gmail). So what happen next is they have to pay really high development fee to migrate their data from Odoo Online to Odoo Cloud Hosting into Odoo Community Version.

Odoo On-Premise, can be dangerous and costly over the time. Odoo uses PostgresQL as database and your system administrator or yourself should know how to backup this database regularly and copy this backups into remote storage for safety. Second issue is cost, now a days running your servers on=premise is costly then cloud, because Cloud Providers optimize their Electric, Internet, Hardware cost.

Odoo Cloud Hosting: is least monthly expensive as small as $5/Month for hosting and if you are also using Odoo Community Edition there will not be any other fee's that you will need to pay.