Top 5 that I can see the advantages of a rooted Android over a jailbroken iPhone:
1) Full Control - You have access to alter any system files, use themes, change boot images, delete annoying stock apps, such as Sprint’s NFL Mobile live and Nascar Sprint Cup Mobile, and other various native applications that might drive you crazy (Footprints, Voice Dialer, etc).
2)Back Up The System - On most rooted Android devices, you can back up your entire system to an SD card, much in the same way you can image a hard drive. This is great if you’d like to try a new ROM, as you can back up your phone, wipe it completely, flash the new ROM, and if you don’t like it, you can just restore from your backup and your phone will be exactly how it was before you wiped it.
3)Save Space On Your Phone
Move cache data to SD card
Moving cache data makes for a speedy system. Rooting allows you to save things like browser cache to your SD card to free up space. Its not too complicated a process, but does take a bit of skill. XDA Developer’s have instructions posted on their forum if you want to tackle the task, it is definitely worth it.
Move installed applications to SD card
Moving and storing apps on internal memory can significantly slow your device down. If you root, you can avoid that completely.
The easiest way to move applications to your SD card would be to flash a custom ROM that just does it for you (using an app called Apps2SD) – Cyanogen ROM is always a good choice.
4)Run Special Applications such as:
Android-WiFi-Tether or Barnacle Wifi-Tethering – Probably the most useful applications you could utilize on a rooted device. They turn your rooted phone into a wireless access point so that you can effectively share your phone’s Internet connection with laptops and other devices near you, using WiFi or Bluetooth.
These apps are better than similar apps, such as PDANet or EasyTether, because you don’t have to run special clients on your computer and servers on your phone you can share a single connection between multiple devices
Super User – allows you to approve or deny root access to any application
Auto Memory Manager – kills tasks you wouldn’t be able to otherwise
Move Cache for Root – move cache for browser, market, maps, street view, and gmail onto SD card
Startup Manager – Clean up android system from system startup to boost system power and memory from the get go
SetCPU for Root Users – Overclocking your rooted device lets you speed up your phone’s processor when you are using it and lets you slow it down when it goes into "sleep" mode. It can either be a battery hog or battery saver.
5)Install Custom ROMs
The Android custom ROM scene started growing shortly after the first Android phone, the T-Mobile G1, was released. The ROMs that were initially available just offered a few tweaks here and there – access to developer only sections of the operating system, debugging information, and things of that nature.
Now, after the release of the G1, the Android ROM community has grown immensely and ROMs have been developed for most of the Android phones currently on the market.
They’ve gone far beyond simple tweaks and can now give your phone an entirely new look and feel. There are ROMs that can make your phone fly by replacing the kernel with hyper-optimized versions or even overclocking the CPU. The possibilities are nearly limitless and attempting to cover all of the features of all the ROM’s available for all of the phones out there would be pretty much impossible. If you’re interested in flashing a custom ROM on your phone, your best bet is to hit the Googles, search for "phonename custom ROM", see what comes up. You’ll likely find at least one forum dedicated to hacking your phone with plenty of information to get you started.
Now, you tell me if a jailbroken iPhone can do any of that other than getting free apps from cydia and pdanet for wifi.