Hello Marianne!
Sorry, I was out yesterday.
First of all, don’t worry about being new to the topic. This is actually a benefit. As we get older, we stick to what we know and stop surveying the landscape for different ways to do things. 
Epicor has/is introducing more options for their SaaS product since I used it. Multiple regions with Multi-company if you have larger facilities around the globe. @timshuwy spoke of an Enterprise SaaS version giving you more control but I don’t know all of the details.
SaaS vs Cloud Provider
With SaaS, you’re on the standard upgrade cadence, which means looking at your customizations and making them upgrade friendly. Any direct DB access is gone and no views, or stored procedures, etc.
With the Kinetic web UI, speed will be better than the .NET client but we still have to work through the newness.
If you’re already an O365 company then Azure becomes attractive since Azure AD can be your identity provider for both 365 and Epicor. You also open up the ability to use other Azure tools like Azure Front Door which lets your users authenticate then jump onto the Microsoft global network and bypass regular internet traffic to get your hosted server. I have not tried this with the .NET client but the Kinetic Web UI should work with this. Again, not sure if Epicor has offered this but it does provide a little extra speed and security.
Not sure if Simon Hall (@hally) is still lurking here but he may know more about the Australian cloud landscape - especially Epicor providers out in the marketplace.
Mark W.