Hey, I just went through this for my grad project. We decided on running Collector on an IPad mini 4. Theoretically you could run that on a IPhone 6 or a Nexus and use it for data collection as well as navigation but I bet that screen would be small. In the past I have used Trimble Juno 5's that have great accuracy especially with the point averaging enabled and do well under canopy.
If you just need rough accuracy (2-4 m) and want a free app check out Trimble's Outdoors App Suite. You might have trouble uploading a lot of points with the free version of the app, but with the paid version (I think I pay them $35 annually) you can upload .gpx files and then send them to your phone. I have used this system for habitat work on private land (hunting lease & cost share) where I needed documentation, but didn't have access to ESRI software or the ability to spend money on a better system and wanted a file I could look at with Google Earth. Also if you need greater accuracy you can use a Bluetooth GPS receiver to increase accuracy over your phone. I don't have any experience with the new ones, but I hear Bad Elf makes a sub meter unit. Cheers, -- *Dan Hoff*