Welcome to the 
community support forums !!
There are definitely a ton of changes occurring between ver. 6. x till 9. x and YES many things will break or might not be available as they used to be before.
But, many improvements had been made as well. However, it is not possible to name each and everything but you can read the release notes (
Since there are not all the release notes on the website for ver 6. x but are available as checked on GitHub while comparing seems to have more than 5000+ commits so if you want to see them view this link.
For the next part of your question i.e. to upgrade from v.6 to v.9, will suggest following this community post as users provided very helpful tips as how they upgraded their server in different environments and how to backup the data.
I hope this helps.