Generally three things:
1. You may have to turn your data over to the cloud. They don’t keep it separate. Your bits and bytes are right next to everyone else’s bits and bytes. What would it take to expose your data to others and vice versa? That is a frontier yet to be explored.
2. You are are hostage to the software vendor’s update whims. They update when they want, what they want. You have no option to take an exclusion. Same with O365…
3. If an upgrade causes logical or interface changes to the apps you are used to, well just… T O U G H ! ! ! And if the upgrade or other circumstances break your process flow… T O U G H ! ! ! Check you SLA.
4. And for all of the companies who had backups in triplicate going back seven years? When they turn it over to a vendor they throw all of the backup and DR plans out the door, because they assume the vendor has them protected. Guess again.
I’m not saying these app delivery methods are bad, but think before signing on the bottom line. Don’t throw away the baby with the bath water.
A. Make sure you have a method in place to constantly replicate your data from the cloud to OnPremises, in a usable format, not an object format.
B. If they allow it, make sure you can get on premises copies of their cloud software versions, prior to upgrades, and that they are usable in case you have to roll back from their cloud to your own OnPrem copies.
C. Good luck!