Online (Saas):

Billed: Monthly

Customization via the User Interface.

Web Services access.

Only Odoo certified modules can be installed.

Themes included.

Implementation/Customization service from Odoo for additional fee.

Odoo Bug Fixing service.

Odoo Security Patch service.

Odoo Upgrade (major version to new major version) service.

"You get access to our scalable cloud infrastructure including hosting, incremental daily backups on two continents, email integration, top notch security, 24/7 monitoring and a control center to manage your Odoo environment. Your Odoo instance is upgraded on demand to benefit from new features at your convenience. You get access to our support by email or live chat in application. Our support teams are available from Monday to Friday, 24/5, in English and French."

On Premise:

Billed: Annually (if you choose the Enterprise Edition).

Customization via the User Interface.

Web Services access.

Any module (Odoo certified, Community written, your own) can be installed.

Full access to Source code with the ability to change anything.

Access your database via SQL.

Themes for additional fee.

Implementation/Customization service from Odoo Partners for additional fee.

Odoo Bug Fixing service.

Odoo Security Patch service.

Odoo Upgrade (major version to new major version) service.

Backups, security, monitoring, management & support up to you or an Odoo Partner.

Odoo also provides a service to help you switch from Odoo On-premise to Odoo Online free of charge if your local database uses the latest stable version.