What is the difference between iOS and android handsets?

Your question seems so vague to answer... Anyways let me briefly cover certain points that might make a difference to most of the people.

iOS devices :

1. A perfect blend of hardware and software.
2. Love the fit, finish ,tolerance and quality of iPhones.
3. Ease of use. The number of layers that you might go to get your functions working is hardly 3 (max).
4. Pixel perfect screens, not to mention about the touchscreen feel that you have on iOS devices. I've used many Android devices and iOS devices until date, but , the touchscreen feel that I get on an iOS device is far much superior to android.
5. One particular feature to note about an iOS device is the switch to turn ON/OFF silent mode. I personally love this feature since it shaves few seconds off unlike any Android device.
6. Even though battery life is based on your phone usage. I personally keep my 3G ON with push notifications enabled 24x7 and I get a decent amount of battery life.Hence,gives me a pretty good battery life (reliable).
7. Never gets slow over a period of time. Comparing the performance of an iOS device and an Android device after a year's of hard usage, iOS device will definitely yield a better performance compared to the same old Android device.
8. None of the iOS device has an upgradable memory card. This has its own advantages and disadvantages. Having a memory card might lead to some data corruption(if you don't maintain it properly), leads to loads junk data accumulation,etc. On the other hand, you can now find a lots of Android devices without expandable storage option, this also leads to better performing Android devices due to less junk.
9. Most of the apps in App Store are paid ones.
10. You got the BEST PERSONAL ASSISTANT (SIRI) here in this device.

I am a die hard fan of Steve Jobs and an Apple fanatic. Ironically, I develop Android apps. :D

On a developer(technical) side of things, iOS device runs on C# (C-Sharp/Objective C), however, the present apps run on customized C# provided by Apple and named as SWIFT. iOS device does not have a garbage collector whereas Android device does have a garbage collector and hence over a period of time the Android mobile devices bites the dust.

Android devices:
You do have enormous advantage of Android device over iOS device.

1. Unlike iOS device (where you have only one phone model), you have enormous models of similar configuration in Android.
2. Unlike iOS device, you have bluetooth sharing in Android, however, lots of apps nowadays are available for cross platform sharing.
3. Android devices generally bite the dust in performance over a span of time (depends on your usage though).
4. Most of the apps are available for free on Play Market.
5. Has a wide variety of configuration to choose.
6. Need to traverse the options beyond the 3rd layer. Makes certain tasks hectic.
7. You have Google Voice Assist here, but never performs tasks like SIRI.

These are some of the major differences between the product.

Both the products have equal amount of pros and cons. Its' about your usage profile and your bank balance to purchase the device that suits your needs.

Again, I've not commented on the security aspects of things above in both the OS. I seriously dislike the fact comparing phones on security basis when every movement in your life is watched over by Google and Facebook and Apple. Every search that you do on Google is being picked by Youtube for Ads and Facebook for Ads. So in this world where technology rules human mind, you cannot talk about security and anyone who fights for the security of the mobile devices/OS are purely dumbheads.