Off the top of my head, I'd like the following (mainly for the iPad as the screen is massively wasted at the moment):
- Split windows (e.g have a browser open on the left, and notes open on the right)
- WebOS style 'fan' application switching (seriously, WebOS is AMAZING, it's a completely unique OS that should have blown iOS out of the water, but didn't due to the incompetent CEO at HP)
- Manual icon movement
- Move the dock
- shortcuts on the top bar to toggle wifi/bluetooth/airplane/etc
- Updated UI
- Allow non-sandboxed browsers (e.g so the likes of Chrome can use their own copy of webkit)
- 3rd Party apps that dont require a jailbreak (i.e allow them to be downloaded via a browser, like you would on Android or on a desktop OS)
- Filesystem access (not a major thing, but would make cross-app files easier to deal with)
- Homescreen widgets (again, allow 3rd party non-app-store ones too)
- Lockscreen widgets (as above)
- Set default apps (e.g set a default mail app, browser, etc)
Some of this IMO is TMI (Too much information). One of the best things about the iPhone (iOS) is the App Store. Locking you into one way to get apps makes sure Dev's get paid, and that your phone is at a much lower risk of getting hacked by some malware off of some unknown or hacked site. This will NEVER happen, as Apple will not change there mind on this what so ever. Not to mention OS X is moving in that walled garden approach to getting your software. Trusting from trusted sources (Apple, and Known vendors) vs from any website.
Widgets are neat for about 4 minutes. They are pretty, and look nice and all, but past that (For me) useless, I need the app more then what a Widget will give me. For what a Widget would do for me, the notification pull down would work just fine. I'm not checking the weather every 10 minutes, or stocks. But, if I was to, its in the Notification pull down. As is my news apps, and messages, etc. So, I'm sure its nice for some, but for me its in the way.
The top of the (tool bar) on Android phones are again, TMI. I used one (HTC) and I don't know what's being represented by what (clearly). Maybe a bigger screen would help with that, but on the phone I used. It was just too much going on there. Not to mention the use of "menu, or other buttons" on the phone to get to things. As this changes from phone to phone. I'd shoot myself moving from one Droid type phone to the next. .....
ahhhh. I'm done. Sorry for the rant, but I literally used my dad's S3 and my Mom's HTC (don't know the model). And both which similar enough to work with going back and forth. The phones themselves aren't. There responsiveness were very different (S3 much smoother). And of course what's on the home screen was different. I'm happy they like there phone, but I actually get to what I want faster on my 4S they they do on there phones.
However, I would be willing to accept the split screen on the iPad feature. As there is enough space to work more then one application at a time, at the same time (for some apps, even iPhone only apps!) Not sure how well that would run, but it would be worth a shot.