Speed and simplicity. For the record I also have a Nexus and iPad. No real axe to grind but Nexus is slower. Have features that allow you to have more control.
Wife also had S3 and now back to an iPhone and far happier with it.. One of kids also has my old Kindle Fire so I have used a few alternatives but Apple do have the slickness nailed.
I know spec for spec Android devices look very favourable but my personal preference is iOS. Super reliable and Apple customer service is second to none IMO. Device value holds up well when want to trade in.
Not massive fan of ITunes tie in but that is now less relevant with wifi and line speed.