A Dropbox competitor just needs to sync my app settings and stuff on top of what Dropbox does. I am gone the instant someone offers me a way to turn on my laptop and have an almost-replica of my workstation. Or upgrade phones, tablets or anything else.
Sync my <breed of device> is a lot better than just syncing some files across them.
Moreover, you could access the same OS using different platforms (mobile vs laptop) and it could behave appropriately. We're already moving towards this to some extent with more and more sync and push services.
NB Just to be clear, I'm not talking about a pure web-based OS and thin client (e.g all of google's products are like this). I mean being able connect to something in the sky that keeps it all in sync whenever you have a data connection.
Disclaimer: I'm ex-VMware employee.
I am remote programmer which needless to say puts me in different coffee shops throughout the city. I ride the bus multiple times a day.
I'm able to switch devices seamlessly as I trek around, and kindle updates my "last known reading location" - go Amazon.
Your scenario is harder but quite exponentially more valuable as we start to see more and more smart devices.