I moved from my iphone 5 to the z3 about a month ago. I've used iPhones for 3 1/2 years now, starting with mthe iPhone 4. In my opinion I love my Z3 so much, the battery life destroys the iphone's battery which needed to be charged at least twice a day.
The main thing i like about IOS is that it is definitely much smoother just compared to any android device I've tested out or used even the Z3. The camera is faster on the iPhone, and so is the keyboard - I'm a fast typer and can feel a delay on my Z3. Camera quality though is fantastic, just the speed needs to be worked out.
Music quality is just as good, im not an audiophile but i like decent music quality.
Apps don't worry about it, go tons of them.
Currently it doesnt have do not disturb mode which irritates me a bit since i get emails 24/7, however I've played around with some sound settings and have sorted it out.
The notification system is much different as well, it doesn't pop up on the home screen, my GF likes that but I don't and downloaded Nils, which completely solved the problem - though someitmes a little buggy - im very picky...
for cases and accessories, i live in hong kong, most cases and stuff are made just across the boarder in china, and there isn't that much compared to the iPhone which sucks coz my gf loves cases - sorry i forgot to mention she has the z3c while i have the z3. don't worry about screen protectors, those are always available.
speaker quality is crazy on the phone, its loud, i love it.
i do play clash of clans, it does drain the battery, but no where as near compared to how much my iphone use to drain.
I have never used a battery pack on this phone, and i say you won't need to unless you're a heavy user, i.e. 5 hours of games or 8 hours of videos can kill it.
Btw i don't use LTE, I know LTE puts a drain on it.
In the end, if you asked me if I would go back to the iphone... most likely no unless the iphone reduces in price and improves its battery significantly.