Yes, battery life is important, also being able to survive a drop on to concrete from head height.
I'd also like good screen readability in sunlight, and good connectivity in fringe coverage areas.
I'd rate all those ahead of screen size, slimness etc. I've not missed replaceable battery or SD card slots at all.
The biggest problem is choice in the market. If you wan't to avoid Apple then your only practical option is Android. Not a happy situation.