I hope I can shed some light on your question, though obviously it's a very personal decision.
I go back and forth between iOS and Android quite frequently. I've sported an iPhone 5 on Verizon since it came out last year, and I recently tried a Galaxy S4, an HTC One, and now I also have a Moto X on AT&T (I have an account with Verizon and AT&T). The point is, I've had plenty of experience with both... though I was originally an iPhone user before Android even came out. All that said, here are my comments for you:
- I completely agree with you about the GS4. My opinion is that it is an uninspired design with poorly optimized software that makes for a sub par overall experience. The HTC One - while having a much better overall experience and superb build quality - is quite large and difficult to use one-handed. I also struggled with poor battery life on the One.
- The iPhone 5 has been a great phone, and is all the better with iOS 7 (which I've been running since the beta came out). I know it's cliche to say it, but it definitely feels right and is just the right size to use one-handed. However, like many others, the Android features and customization are very alluring, especially as iOS grows a little tiresome (even with the iOS 7 changes, it's still basically a grid of icons). If you already have quite a few other iOS devices, there's nothing better than an iPhone to tie them all together.
- That said, there are ways to use iOS and Android devices in conjunction with each other without too much hassle. For example, you mentioned sharing a calendar. My wife and I share a calendar and she as an iPhone and I am using Android. By switching everything over to Google, you can easily add Google services to the iPhone (though not the other way around). So export your iOS calendar to Google and then you'll be able to share your calendar just like you currently do. Your wife won't even know the difference once you get it set up. Contacts too can be easily synced with iOS, so imo it's better to just use Google services and then you'll be able to switch between iOS and Android much easier.
- Regarding the Moto X specifically, it is probably the closest thing to an iPhone you're going to find on Android. Though the screen itself is larger, the phone doesn't feel much larger. It's about the same height, though a little wider with more screen real estate. The build quality of the X is quite good, much better than the slimy feeling that the GS4 has. And with a nearly stock build of Android, it is not weighed down by unneeded software features like you find on the GS4 (and even the One). It truly feels almost as fluid as an iPhone in actual use, which is saying a lot IMO.
- Regarding storage space, you learn to adapt to the lack of an SD card. On iOS, most of my space was taken up by games. I rarely play games on Android, so I don't even come close to using all of the storage space. There's plenty of memory on the Moto X for photos and videos as long as you are willing to download them to your PC once in a while and clear them out. You can even do this wirelessly with Android/PC software. As for music, I have switched over to a music subscription service (Google Play Music is pretty awesome, as is Spotify). This has cut down on the amount of storage I need, though I can still download songs/albums for offline use whenever I want - and it's easy to switch them up when you need to clear out space. If you can get a Moto X with 32GB, definitely go for it, but even 16GB is plenty if you are conscientious of your media habits.
- And finally, the Moto X is the most personal phone I've even owned, mostly due to the customizations that I was able to make at Motomaker.com. I don't know what carrier you're on, but if you're seriously considering the switch, I would suggest waiting for Motomaker if you aren't on AT&T. Having a phone that looks the way you want is something unique with great satisfaction. The Touchless Controls and Active Notifications are just icing on the cake. The REAL appeal of the Moto X, in my opinion, is the overall hardware design of the phone, the customization, and the buttery smooth nearly-stock Android experience.
My recommendation is to give one a try and just return it if you don't like it. You've got nothing to lose other than perhaps a restocking fee, which is a small sacrifice for the ability to try before you buy.