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GPS enabled phones actually do remarkably well considering their size and all the other things they are doing. Iphone lasts longer than Android but I hate Iphones (its personal). A external battery pack will keep you going all day. A phone will give you accuracy to about 5 meters in ideal conditions...open sky, clear weather, no trees or mountains nearby.
As far as a handheld GPS goes, they were designed specifically for this use and they do it well. They come with features and apps that your phone does not. Garmin set the standard to which all other GPS units are compared. A good Garmin, WAAS enabled GPS will give you accuracy to 3 meters, again in ideal conditions. The US Government Satellites provides a signal that is accurate to 4 meters 95% of the time. If you stand in one spot for a while the GPS will log position coordinates and average them to give you accuracy down to 3 meters. Civilians will not get better than this, at least for now. For some reason a canopy of old growth timber above you will really mess with the signal. For laying out a claim you need a feature call "waypoint projection". This allows you to set up a destination waypoint that is a specific distance and direction from the previous. You program the claim corners at home then go out and just follow the GPS.
I currently use a Garmin Montana 650T and I love it. I can project a corner, find it and plant a post. Then I can photograph the post with the built in camera and the GPS coordinates will embed into the picture. My previous GPS was a GPSMap 62CSX. It was a work horse and is a fine unit. I upgraded because I wanted the larger screen. A 62 will still cost you $150-$200 used.