The iPhone 5s and the Samsung Galaxy S4 are the undeniable kings of smartphones. If you're looking to get work done, which one is better?
Screen quality and size
In smartphones, when it comes to productivity, screen size matters. A larger screen makes working with productivity apps such as spreadsheets better and more useful. And it makes Web browsing better as well. Here the Galaxy S4 clearly beats the iPhone 5s. It's got a 5-inch screen, compared to the iPhone 5s's 4-inch screen, and that makes for a surprising amount of extra real estate. It's got more pixel density as well.
Productivity apps require typing and data input, so a phone's keyboard is extremely important. Here again the S4 comes out the winner. It has an entire row for numbers, so you don't have to switch back and forth between a letter keyboard and a number keyboard as you do in the iPhone. In addition, the Samsung keyboard allows for much faster word input because you can swipe your fingers across the screen instead of having to tap. And it's easy to change the Samsung's keyboard to another one as well.
The iPhone 5s wins this round. iOS is simple and straightforward. You'll never find yourself lost in a rat's nest of menus, or trying to get back to where you used to be. Android is more complicated than iOS. Making things worse is the confusing TouchWiz interface Samsung layered on top of it.
The S4 wins by a mile here. There's a reason Android is more complicated to use than iOS -- it gives you far more ways to customize it. That means you'll be able to get the S4 working exactly the way you want it.
Apps and ecosystem
Both iOS and Android have no shortage of apps -- multiple hundreds of thousands each. As for which has better productivity apps, that's a toss-up; no winner there. When it comes to the entire ecosystem, though, the nod goes to Google, with its Google Drive, Google Docs and other services. Yes, it's true that these are commonly available as iOS apps (and on the Web) as well as Android apps. But improvements to them will inevitably come on Android apps first. So the nod here goes to Google.
The winner? All other things being equal, the S4 will make you more productive than an iPhone 5s, given its its better screen and keyboard, and customizability, and superior ecosystem. If you're a lover of all things Apple, though, you'll probably want to stick with the iPhone 5s because you've likely got your data in iCloud and are used to the Apple way of working.