Welcome to the Note 3, a real work/pleasure phone.
I think the main difference is the way you can customize the phone.
Custom keyboards (swiftkey), custom notification (floating notification), sidebars (smart taskbar 2) on which you can launch apps from every other app.
But also the integration between apps. You can share texts between apps. So select a text, and browse this on the internet, or to translate to another language, ect.
You can even have floating windows (floating widgets app), so you work with more apps at the same time. Or have multi window, to watch a video and take notes, or browse the internet at the same time.
Personally (Note 2 user), it's all in one phone. On work i can take handwritten notes on meetings. Keep my contact with full information. Or just play with it and browse youtube movies. Or watch a movie while working out. The big screen is ideal for all of this.
For many of the iphone app, there are good Android apps or replacement apps.