I have iPhones uptil iPhone4 and switched to Notes2.
Battery life of Note2 is EXCELLENT! Since I owned it, there is only one time a low battery situation ocurred. ALL my iPhones before make me nervous about finding an outlet whenever I get out of my house or on a trip because I ran out of juice so many times when I am in much need of talking to my clients. Even when I just go out for dinner, I look for a spot where I can find an outlet. As for rebooting issue, I believe it is more about the apps ppl uses on their phones than the OS/phone themselves. I have exactly the opposite issues with those who claimed they need to reboot droid while iOS never fails. If you have read my previous posts since I owned the first iPhone til the last one, I have to reboot my iPhones frequently and sometimes even the AT&T reps cannot restart them for 10 minutes. Only once, the s-notes in Note2 saying the app stopped and restarted the app by itself-still never need to reboot the phone at all.
The iOS seems smoother for consumption purposes. If you install the newest iOS, it's getting similar to the droid and starting to deviate from the original iOS, so may still need a little getting used to. To me, any iPhone screen is way too small for productivity such as writing notes in a meeting and writing down thoughts while on the road or looking thru spread sheets of quotation. Reading news is much easier with the Note 2 than any iPhones I have or encountered including the iPhone 5. The longer of iPhone5(s) over the previous ones do not help in making more info on the screen at a comfortable size. However, with the much increase speed(at least on spec) of the new A6 CPU in the 5s, it should be a very good gaming machine.
The Note2 is big, so sitting down with it in a pocket is VERY uncomfortable because I always fear I will break it when it's slipped at the back pocket. So I have to put it on the table. That works out for me, most of the times anyway, as I can see the notifications as it comes right up in front of me. People claiming it cannot fit jean pockets are almost ridiculous as it does fit into my slim cut jeans while I am only a petite guy.
Never serious about games on phone, so no idea which one is faster or smoother in that category.
So my take is that if you use your phone no more than a phone or just read msgs, and gaming, then go for the iPhones because it's very seamless while if you need the phone to do any productivity or love movies, go for the Note 3.