In my opinion, obviously, it’s the first one.
The others aren’t webapps, but web pages turned into something like an application. They’re a better way to use web pages, but they aren’t actually like native applications.
A WebApp is developed as a WebApp since the start by its developer and has a good platform integration.
A Chrome WebApp doesn’t have a good platform integration and isn’t developed as a WebApp by its developers.
An Ubuntu WebApp has a great platform integration (but it runs into a Firefox window and not in a chromeless window) but isn’t developed as a WebApp by its developers. Moreover it uses an Ubuntu-specific API (actually, Unity-specific).
A Firefox WebApp is developed as a WebApp by its developers and has a good platform integration (as much as it’s possible with cross-platform features) that will most probably improve in the future. For example the Firefox WebApps will have custom menus (and so on Ubuntu they will have HUD support).
However, I wonder why Ubuntu developers didn’t contact us in order to create their webapps using our method (so they’d have chromeless windows, for example).
to Jair: You can find instructions how to install precompiled Firefox/Iceweasel versions (esr,release,beta,aurora) for different Debian releases (also squeeze). Pick right choices from dropdown boxes, and this page tells what lines to put in sources.list http://mozilla.debian.net/
to Frank: That isn’t true. You can own the application and you can own the data, WebApps aren’t different from native apps.
WebApps don’t necessarily save your data on the cloud, but they can use local storage APIs (for example, IndexedDB or DeviceStorage).
I’m interested in your comment about custom menubars in Firefox webapps. I didn’t realize that such a thing was planned. As the author of the addon we ship in Ubuntu to export the Firefox menubar to the shell, I’m quite interested in seeing something like that.
I wish I was able to give an answer for your last point…