I have been experimenting with SAM Broadcaster for quite some time now and I have a few questions.
Can you achieve a better sound using the Pro version since it supports plugins like Stereotool while the cloud version does not?
In theory, yes. If your music files are already of proper quality, though, you should be fine sending them out as they are.
What about crossfading settings? I feel like it's easier to find the right settings with the pro version.
That's mostly a matter of taste. The Pro version has more customization options as you already noticed yourself.
Finally, do you have to deal with running updates and or patches on a VPS server? (Thus risking having dead air is the cloud version more stable)
A VPS is just a computer in a datacenter. Windows needs to perform a (virtual) reboot in order to install updates there as well.
Are you forced to install them? No.
Should you install them? Yes! Even more so on a publicly reachable VPS than on a local machine.