<Galaxy S4
Pros: 1. Better camera
2.Considerably larger screen (AMOLED) with higher resolution and ppi, higher contrast(depends on personal preference, I prefer iPhone 5 screen with lower but adequate contrast that makes images more realistic. AMOLED doesn't use battery power when displaying black since it completely shuts down backlight in that area)
3. More Samsung apps that bind with your phone, I don't think you can uninstall them easily if you deem them unnecessary and a waste of space.
4. Longer battery life, battery with bigger capacity.
5. NFC technology, you can share file wirelessly with another NFC enabled device within a close range.
6. More customization on system since it's using Android.
7. More minor functions, such as you can record using both front and rear cameras simultaneously and it can trace your eyeballs so things scroll automatically.
8. More powerful hardware, depending on where do you purchase, it's either using Snapdragon quad core or Samsung Exynos 5 Octa(8) core.
9. Able to download apps and basically everything from the Internet source/browser.
Cons: 1. The Octa Core processor is quite a waste, only 4 cores can work at the same time. And performance isn't that crucial, it's more about app optimization.
2. Slightly heavier than iPhone 5. And BIGGER, which may not fit the size of your hand.
3. Some people criticize that its case is made of plastic, but I don't think that is a huge issue because plastic is also lighter than most other materials.
4. Poor display of white colour on screen, when you compare it to other non-AMOLED screen it's more like grey.
5. Poor display under sunlight, another disadvantage of AMOLED as the backlight of screen isn't strong.
6. Poorer app quality compared to iOS. This, however, depends on your preference about Android and iOS. Android has true multitasking and more customization, and some widgets are quite useful, allowing fast switch ON/OFF of wifi, Bluetooth, etc. whereas iOS is considerably smoother, more easy-to-use interface and better overall app quality.)
<iPhone 5
1. Smoother system, less lagging when you scroll etc.
2. Easy-to-use interface (actually what are the advantages of iOS are also advantages of iPhone 5)
3. iCloud backup, saves all photos, contact, recorded videos etc.
4. Lighter than Galaxy S4.
5. Better app quality overall.
6. Can only download apps from AppStore, of which many you need to pay. You can't download cracked apps or free apps like Android unless you jailbreak, which is quite troublesome sometimes.
7. Poorer camera compared to Galaxy S4, but only slightly.
8. If you jailbreak, you can also have a lot of customization on system but also making it slower and less battery life.
9. You can't change battery on iPhone, you can do that on Galaxy S4.>
There are many more things I haven't summed up, but if you want the easy way choose iOS, Android can do more sophisticated stuffs but also require skills.