If you upgrade (to the Squiz DXP, or the v16 multi-tenant environment (prob what you are calling FB SaaS) when you move you should be able to run and schedule your own updates. I'm not sure what your current environment is, but if it's a standalone server (like you normally get if you host your own, of if it's hosted in Squiz Cloud) there are a lot of advantages you'll get by moving.
The key ones are:
- The environment is multi-server, with multiple query processing servers that are separated from admin - this means that if one of the servers goes down your public facing search won't be affected. It also means that query performance is not affected by any updates that run on the admin server.
- The environment is managed - any patches that are released are automatically applied in a timely manner, and if you're on the Squiz DXP you are always kept on the latest release.
- The environment is actively monitored for a number of different things.
- The Squiz DXP and v16 provide a library of plugins that you can use to extend your search.
There are some things that are restricted, due to the environment being managed but these shouldn't really affect your ability to manage and use your search and the advantages really outweight any restrictions that are enforced. The best thing to do would be to get in touch with your account manager and organise a session where you can ask any questions you might have.