To me, a Jailbroken iOS seems infinitely more powerful.
Simply because, once you get jailbroken, you have native access to the OS and the Darwin Kernel. You get full access with all read-write permissions to the system files.
In a rooted Android device, you still need to run busybox and allow permissions. Busybox seems like a hack to me.
Also, with Android, you're still dealing with the Android window manager and the Dalvik JVM. On iOS, you don't need to run Cocoa or the use the iOS UI. Some people launch their own X11 Window manager and it is like running a full blown UNIX. Sure, there is no touch and stuff but the fact it can run it is compelling.
With an iPhone, you can compile anything that runs on Darwin to Darwin ARM.
E.G.
A full blown Apache/ MYSQL and PHP stack can run on the iPhone.
Tutorial: Apache Webserver With PHP 5.2.3! | iPad, iPhone, and iPod touch forums | iFans
Nitroware iOS Web Server | iOS Apache | iOS HTTPD Server: Welcome!
Thats pretty powerful stuff. Once you get console access, it is like running a OSX box.
You can compile native X11 apps and run them on iOS.
Running native X applications locally on your iPhone On the third side
I mean, you can download any GNU app, and compile it with GCC on the iPhone itself. That is a full blown OS not crippled by anything.
Let me repeat once again, you can download source code onto the iOS device and compile it with GCC on the phone itself.
Some links and source:
Compile C applications with gcc on iOS 4 (iPhone) IT News, Tutorials, Solutions – SYSTEM HALT
https://tootallnate.net/how-to-set-up-gcc-on-ios-4
Seriously, the fact you can run a full Apache/mysql stack on a portable device is pretty freaking cool.
On Android, the only benefit to rooting for me is the ability to load new rooms, run OpenVPN, run Samba and wireless tethering.
However, the rooted app seems like hacks. For example, Samba Filesharing on Android uses an Android app that is VERY LIMITED.
On iOS, with Samba (for iOS) you can SSH right into the phone, use your command-line wizardly right in the /etc folder and start/stop services like you are on a real UNIX machine.
See, that is why I said it was infinitely, has the potential to be more powerful.