After trying several apps and stand alone GPS's, my favorite by far is Motion-X GPS app for iPhone. I have an iPhone 6 Plus, so the big screen is definitely a nice feature. I think the app is very intuitive, and feature filled. As far as accuracy goes, assuming you let it locate a sufficient number of satellites, I can't see an appreciable difference from my Garmin handheld. That being said, phones use both triangulation of cell signal and GPS for positioning, so if an adequate number of sats have not been acquired, accuracy can suffer. If I'm going to be in an area of poor cell coverage, I download and cache the maps for that area ahead of time.
I agree about the battery issue. If I'm going to be using my GPS for long periods of time, I use a "Dual xGPS150", a standalone GPS receiver available on Amazon and elsewhere. It is a standalone device with its own rechargeable battery, and it connects to your phone via Bluetooth and overrides your phone GPS. It comes with a armband, or you can fasten to your coat, pack, etc. Since it is no longer using the phones GPS chip, phone battery life is greatly extended. Since it's not in and out of my pocket, and always linked to sats, the accuracy is more consistent.
If I'm in an area where safety is a concern, I do carry a backup Garmin in my pack. That's probably not a bad idea regardless of what device you use. I like the convenience of always having my GPS, waypoints, and trails with me, and the ability to share or move easily via email or text.