The Sony Xperia Z1 Compact features a quad-core 2.2GHz Qualcomm Snapdragon 800 processor, while the iPhone 5S has Apple's 64-bit A7 processor.
In the real world the smartphones are pretty evenly matched in performance, with the Xperia Z1 Compact and iPhone 5S both delivering all-round smooth experiences. However, we did find the iPhone 5S slightly snappier at opening and closing apps, and found it handled multitasking slightly better than its Sony-branded rival.
Winner: iPhone 5S
Despite their similar performance, the Sony Xperia Z1 Compact and iPhone 5S mobile operating systems couldn't be more different, with the handsets running Google's Android 4.3 Jelly Bean and Apple's iOS 7, respectively.
It's always hard to compare Android with iOS, because most smartphone users already have their favourite, with some favouring Android's openness and ability to customise, and others preferring the simplicity of Apple's iOS.
On the Sony Xperia Z1 Compact, Android 4.3 Jelly Bean is coated with Sony's custom skin that overlays the stock user interface with the firm's custom apps and widgets. Saying that, Sony's custom user interface is much less obtrusive than Samsung's and HTC's skins, but it still has more of a learning curve than Apple's iOS 7 mobile operating system.
Sony has loaded the handset with custom applications though, which we didn't find ourselves using very often, opting for Google's alternatives instead. These include Sony's Music and Video Unlimited services and its dedicated Playstation app.
Apple's iOS 7 mobile operating system is also loaded with proprietary apps, such as Newsstand and Stocks, that you're unlikely to find yourself using, but it offers an all around much simpler, minimalistic experience than Sony's custom Android software.
However, iOS 7 isn't for everyone, with the flat design and motion effects having irked some iPhone users following its release.
Next: Cameras, battery life, storage, price.