Thanks to XD's warning I was prepared for this when the orange message flashed up! Good news, it doesn't insist the switch be made immediately, but I did anyway. Bad news, I found the online advice confusing. I think this is because the page is mainly aimed at new users who make the choice before downloading the software, with existing users considered as an aside. Or perhaps it's an intelligence test – I failed. After flapping about trying to understand what they wanted me to do, it turned out to be a simple change to the Account, not the software. The package doesn't need to be reloaded, and everything carried on as normal. Updating the account on one machine also updated the other. The advice suggests leaving 30 minutes after switching before restarting F360, mine worked OK immediately.
The differences between Hobby, Student, Small Business and Professional licences are more pronounced. The Hobby licence is single-user (it doesn't support teams collaborating on the same project) and a bunch of add-on tools I've never needed are only available on the grown-up versions. Fusion 360 itself remains fully functional.
Another recent change is causing me more grief, fortunately not serious. Most of my sober CAD work is done on a desktop with a big screen, but I also play with a laptop in front of the telly. Previously, both computers 'just worked' but this is now blocked. Wouldn't be an issue except logging off F360 seems unreliable: firing up the second computer complains the first is still in use, and a screen pops up to kill the session even though the first machine is switched off. Wastes about 30 seconds of my valuable time!
Dave