So I have a iso install on my USB drive. The purpose is to use this as a drive I can use on multiple systems. It is my understanding though that when I do a full install - the hardware compatibility will vanish (as it is configured for the current system).
If I am wrong, that is great. If this is true though, is there an a ability to create “Hardware Profiles”. AKA sets of drivers grouped that I can swap between depending on the system?
Yes, the hardware related configurations and abilities will be different based on the hardware of the machine (live boot might (should) not have the same requirements or abilities due to the mobile nature of the OS and being generally compatible with most machines you could/would use it with/on. You could always partition your harddrive and start small so that you may return to your original OS if that is the main concern but it sounds like you are fairly familiar with it and enjoying it as much as I am! 
See I keep hearing people talk about live boot - but everything I read says that live boot can become unstable once you try to update it etc. Is this no longer true?
I’m not sure about the stability as I do not have the need to live boot so I choose to just install, but I believe it is typically going to be less functional as it cannot fully utilize whatever hardware you have on the machine. I would say that stability is not the main concern per se, rather your needs from the OS is a stronger deciding factor. Here is a link to an Ubuntu discussion regarding some of the pros-cons of such a setup which should apply for the most part and hopefully help you decide what would serve you best! https://askubuntu.com/questions/779260/live-usb-or-live-install-better-for-my-needs