both Android and (too some extent) iOS use .deb files. While the phone versions of the apps may be impossible to use, but could the tablet versions be converted? One of the reasons my friend keeps giving me against Ubuntu and Linux in general is the lack of really good software. If we could tap into the Android apps though, it would really open up possibilities!
If you use a Jailbroken iPhone, you'll notice that all cydia apps are in the .deb form.
And yeah, I'm aware that there is really great software for Linux, but sometimes I feel it lacks, especially in the gaming section (Fingers crossed for OpenMorrowind). Imagine being able to run Angry Birds, Fruit Ninja and Plants vs Zombies natively on Ubuntu. Or, imagine some of the great Ipad Apps like Dragon Dictation or heck, even Infinity Blade!
The possibilities would be endless.
Best Answer
You can run the apps from Android with an Android emulator, see this was asked before: Can I run Android apps on Ubuntu?.
Maybe you can re-compile the source of some app to work on linux.
Would you explain better the similarities you found between deb and apk?
Finally, about the quality of apps, I think it is a matter of opinion. In my opinion, linux has the greatest softwares available (thanks to the community cooperation and efforts).