Is the iPhone anything like the iPod Touch? I had the 1st, 2nd, and 3rd generation Touches. Over time, I really began to hate the free apps with their 'Lite' versions and endless in-your-face ads. Anything decent needed money. And the devices used to overheat. And lag. And the batteries seemed to have really short lifespans if I used any of the devices to play games. And then apps stopped being supported for the earlier generations. After that, I've had a healthy dislike for anything Apple. I seriously felt like it didn't seamlessly fit and add to my life, it would just annoy the Hell out of me. If the iPhone is anything like that, I'd run for miles in the opposite direction.
I have a Samsung Galaxy S5 which has been going strong for over two years. The only wonky thing is the camera which used to focus when I first bought the phone, but now it needs to be smacked around before it takes unblurry pictures. I've noticed my battery doesn't hold charge as well as it used to, but everything I use the phone for still works smoothly and without any issues. Some free apps have obtrusive ads, but I actually don't use my phone much anymore so it doesn't bother me too much. Most of the time it's just for mail, music, YouTube or news.
All these touch-screen phones look the same to me, so there's no 'special shape' that I'm immediately drawn to. I did like the metallic blue backing of my phone, so that was a no-brainer and the only differentiating factor for me. Make sure it fits comfortably in your hand. Even the S5 is pushing it for my tiny hands, I need both hands to use it (one to hold, one to tap) without dropping it. Or if you're not going to be holding it much, then get a nice big screen for whatever you're planning on using it for. My aunt has a Samsung Galaxy Note 2, and it feels so spacious on the screen, so much room for everything! It looks a bit ridiculous when she holds it up to her face to make a call though.