My wife was a long-time average droid/android user. She switched to an iPhone 5 because all her friends had it and hates it. She still can't make it thru the day on a single charge.
If you want something that'll last the day, get a Note 2. I can get thru 7am - 9pm with 8% left on a single charge under moderate usage (phone, email, web, ebooks, YT, G+) with Touchwiz and no ATKs.
There's no way I'd go to an iPhone and be locked into the world of apple. Android is so much more robust, so many more options. Sure the iPhone is pretty, and it may be 'hip' to own one. Forget it. Deal with the power issue like the rest of us. If you are going out and about for a full day, bring your freakin charger. It sucks, but that's android (for now).
I'll echo Adam74's comment and post above. I will also add to the comments by iamjoe by saying that these phones use a battery which actually lasts longer over time (lifespan, not runtime between charges), but giving it short "interim" boost charges whenever you are near a power source. For me, I have a car navigation dock and when I am in the car, the phone is on the dock and being charged. I carry both a wall adapter & cable, and also a portable power pack (*RAVPower Dynamo-On-the-Go RP-PB07 Super High Capacity Power Bank (10400mAh Capacity / 1A & 2A Dual USB Output) for iPod, iPhone, Smartphones, Digital Cameras, Tablets and E-Books*), which are ready to jump into action at anytime. My office desk as the desk docking station and the phone is there during the working hours, unless I'm roaming around the office or out to an appointment.
By giving the phone even just one short (.5 - 1 hours), boost charge in the middle of the day when near a power source, it may be enough to bridge the gap and get you through the rest of the day without dying. Since these phones typically take from about 3 hours to as much as 5.5 hours to fully charge from a fully discharged state (my Droid RAZR MAXX has a 3,300mAh battery so it's 5.5 hours for me), you can do some quick and dirty math (best case scenarios and consumption rate averaging for illustrative purposes);
3 hours charge gives 16 hours runtime on a battery that's 1,750 mAh...
So 1,750/16=109.375 mAh/hr discharge rate...
And 1,750/3=583.33 mAh/hr charge rate...
5.5 hours charge gives 16 hours runtime on a battery that's 3,300 mAh...
So 3,300/16=206.25 mAh/hr discharge rate...
And 3,300/5.5=600 mAh/hr charge rate...
...And conclude that a one hour boost can yield from 3 to as much as 6 hours of extended runtime, and it is actually good for the battery as well. It is on the other hand very bad to run the battery down to the near zero remaining charge depths as this stresses the battery and WILL result in a shortened lifespan, as well as put you at risk of the battery and phone becoming unresponsive to a charger at some point due to deep discharging (white light of death, bootlooping, etc.)
The iPhone is not the solution and it will not provide you with a better Battery. If you do go down that route you will need a Battery Extender and this is a great one.
But, I would stick it out with Android either Samsung or Motorola and see which works best for you.
Real easy answer to your question. Get an iPhone and you won't have any problems, only because you can't do anything on the iPhone. For example, try downloading something from a 3rd party website. Try watching the desktop version of YouTube. Try watching any flash video from YouTube, or any other site for that matter. If you have your own website, try updating it from your iPhone. I can manage my website on the fly from my android, and even on my daughters' semi-rooted Nabi tablet! Can't do that on an iPhone.
Note 3 is probably due for release in September. Might want to bide your time provided you can handle the generous dimensions.
Note 2 is far and away the best phone I've ever used. Plan to upgrade to Note 3 at earliest availability.
I run my phones at full speed and maximum brightness and never never fuss with power management. Simply carry a spare battery which can be switched out in 30 seconds max.