I use my Galaxy S4. A matte screen protector combined with using my hat so the phone is in shade when viewing seems to do the job. Even though it uses more battery, I keep the brightness all the way up, since I'm only turning it on for a few seconds every now and then.
Going from memory, the latest iphone has the maximum brightness overall, but the Nokia Lumia fared best in outdoor viewing tests (not sure the Nokia has the same app availability as iphone/android though). The latest Galaxy S5 also does fairly well in sunlight, and was the best at night (allows for lowest brightness setting). Some fairly detailed testing and specs can be found on the web. The nice thing about the Samsung line is the availability of 3rd party oversize batteries. I have a battery that is 3x the stock size, so I can get through 4 days of use with only the GPS turned on and cached maps in the Backcountry Navigator app, as well as continuous track logging in the Google MyTracks app. I don't use it as a camera/mp3/etc though.