It depends which kind of security and which provider.
I would trust Microsoft more on patches/configurations for an email system than something which is managed on premises. You need to have really good people to maintain a good level of security. Not only technically good, but also with a string cold management that will force updates even if it means the CEO will not get his maol for 15 minutes - and say that this is life and that the discussion i sover.
On top of that, MS would (I hope) install patches on their customer-facing systems in advance of an official patch release.
The above applies to the majority of large SaaS services.
Now when you have a "Platform", a hoster that requires you to bring in knowledge and not only data then it gets dangerous. You need to maintain the security of what you bring in. This can be an OS (your "Platform" provides VMs), or code (your "Platform" provides code runners). Unfortunately, when a company moves to the cloud, they sometimes forget to do this assessment and end up with monstrosities they installed themselves (which is not different, security wise, from having it on premises - augmente nu the 7B population that potentially has now access)