What can't you do on iOS that you can on Android?
May or may not be important to you but what I do on my Note 3
I have replaced the stock dialer
I love selecting different launchers. Nova is my current daily one, but I also Use Themer now and then. Simply flip back and forth to completely change the look and layout of my phone depending on my mood. Silly perhaps, but there are days where I'm at work and want all my works apps and information a certain way, but on weekeneds or the evening I can flip and have mostly my personal, music, workout, social media apps more on top of mind, etc. Jeckle and Hyde so to speak.
I use PowerAmp Pro for my music player
I use Llama for location based services to automate all kinds of things. I really like this as when I work from home, I want my phone set up one way, when I work remote at my office I want it another. Things that change for me are numerous and they are all fully automated. From Blue Tooth, to brightness, volumes, call forwarding, etc.
I also enjoy having more than just one way for notifications. I use a completely different app for notifications that I like better than the stock one. I also use a third part SMS tool. Options, options, options, that's why I like Android.
Not to mention I love having a fully google integrated phone from Google now to Google +
At the end of it, if you like iOS and are fine with having many if not most of the things you do on your phone dictated by them to you and can live with that then by all means stay Apple. Me, I prefer to try new apps and services that match what I am looking for. It's not about colors and shapes, but the function of even core applications.
On top of many of things I've already listed....
Dialers
Email
SMS
Calenders
Notification bars, pop ups, reminders, etc.
Notes or To Do Lists, etc...
Again, there are multiple very good and solid choices. So many that like I said, I can customize my phone based on what I'm doing that day or even how I feel. My Phone, My Way When I want it. Many of the changes can be made to automate too. It's so nice to setup a configuration tool that can Taylor things based on where I am.