I have an iPhone, I was using it this morning with no problem, looking at wait times, reservations, etc (we were planning when to book our FP's).
PP mentioned a upgrade for the app for iPhone which will be released soon. Android will be released later this year, maybe September?
My iPhone is over 2 yrs old (it is a 4S), I have a Mophie case that is also an extra battery pack. It works great if I need to extend the battery life. I have not had an issue before, but have not used MDE in the park. You can turn the extra charger on or off, depending on where you want the phone to be powered from.
I have been using iPhones for 4 yrs now, and really like them. I have friends who like their android phone, although she had problem with the app this morning on her phone while we were planning. I think she has the note or something, not as big as the galaxy.
If you do go with android, be aware since it is an open platform, a lot of the manufacturers and the carriers will add their own software (they call it bloatware) which affects the amount of memory actually available for your use, if that is something that is important to you. I have heard quite a few complaints about that recently.