Personally I think you would be happy with a windows phone--especially with the new features being added in windows phone 8.1. Let me hit a few highlights.
1. Similar high level security as your iPhone. The OS architecture is built on security. With so many security issues in the 90's, Microsoft changed gears and focused on security at the expense of all other product development. They practically wrote the book on quick patches and updates to solve vulnerabilities. But beyond that, the winRT OS on which windows phone 8 is based on the same principles as iOS. Google's Android OS is more like winXP. You can pretty much do anything you want to customize the phone but at the expense that someone else can easily gain the same access with the lax app publication process. With iOS and WP8, Apple and Microsoft validate the apps so you know they are safe.
2. Syncronization If you like how iCloud works you will likewise enjoy how windows phone utilizes OneDrive. You can backup your documents and settings to OneDrive and access your files in other places. So, for example, you use OneNote or Office on your iPad, you will be able to see those files on your windows phone and even edit them if you need to. It's admittedly more difficult to edit office docs on a phone but setting up a shopping list on your windows phone using OneNote is awesome. Furthermore, if you use your iPad to make notes on OneNote, it automatically syncs with OneDrive meaning that if you are on your windows phone you will be able to pull that note and review it elsewhere. You can even access those notes through your web browser on a computer if need be like you would be able to with iCloud.
3. The App Situation Most people are concerned with the apps on windows phone. I agree that the apps are not as I would like but I anticipate everything getting better. Most of the apps you need you can find. The apps are not always identical to apps on iOS or on Android but I don't think it's because app developers don't want to be on windows phone. I think it has more to do with older polices that added overhead costs to developers like pricey developer licenses and a lack of integration with windows RT (two different stores and development paths that will soon be similar or the same). With android and iOS, you can make an app for a phone and allow it to scale up on an iPad so you build one app and it works on both. Windows phone and windows 8 haven't been like that but will be soon. Consequently, the frustrations that a lot of app developers think about when they have to build a windows phone app are gradually being removed. I think with the new leadership at Microsoft you will see an improvement of the app situation.
Like many others have pointed out though, the app situation is also not quite a "situation." You can pretty much find an app to do what you want if you need one. Just think about it. When there's a gap in the app system, new app developers who see a need jump to make a name for themselves by creating 3rd party apps that rival even the 1st party apps on other phones. Rudy Huyn, for example, has made several 3rd party apps that people love. I know his name because he has capitalized on the slow pace of 1st party developers. You might miss some niche apps but you may also find someone who makes a better version of that niche app too.
4. People Hub and Account Integration This last one is probably my absolute favorite aspect of the phone. I can sign into multiple accounts like Facebook, Skype, outlook, Google, yahoo, and etc. and I can see everything about a person in one place. For example, I may have said something to my friend but I can't remember if I said it by phone, Facebook chat, text message, email, or etc. but I can go into the People Hub, find their name, look in the history and see all my recent activity with them. I can see my Facebook and text messages right there and review them. I can see if they called me before or after I sent them a particular email or after a certain Facebook or text message was sent. I can see the most recent emails from just that person without having to go into my email app and search for them. Plus, I can pin their profile to my start screen and I will get a notification if they send me anything on any of my accounts. Likewise, I can make a group for people like my family or coworkers and pin that to the start menu and then I will see if any of them have sent me anything on the same live tile.
And none of that is even getting into the hardware differences. From a 5S you will likely get a bigger screen (although maybe not the same resolution), a more durable phone, and a better camera. I've lost count of the number of iPhones I've seen with cracked screens (5C, 5, and 5S) included. My Lumia 920 fell face down from 3 feet onto a tile floor without a scratch. I've also dropped it out of my pocket a time or two without issue (I have a thin incipio case). You will find others on the forums with similar experiences or even worse.
I think if you get a windows phone you should be nervous because it is a new phone with new things to learn but you'd have the same situation getting an Android phone or upgrading to a new OS. However, I don't think you will be disappointed with your new phone as long as you go into it with an open mind. It's not going to be iOS and there will likely be things you miss about iOS on windows phone but you will likely find new things on windows phone you wished iOS had.
Good luck and I hope I've been helpful