I bought a Droid Maxx and like it enough but came across battery cases that I did not know about, like the one Incipio offers @ [Only registered and activated users can see links. Click Here To Register...]. Would an S4 with this attached be better than an Droid Maxx, due to the screen and other performance specs. I had an S3 but it frooze on me often within first week and once took 30 mins to restart. Kinda skeptical about Samsung quality.
Re: Battery Cases
Sorry to hear about your bad experience with the S3.
It really depends on how you use the device. The Maxx is a good device and battery life shouldn't be an issue unless you use the device often and intensely. On the flip-side, the S4 is also a good device but stock battery life is probably not the same as the Maxx. It's really going to come down to the device you like the most since their is a battery solution to get you added battery life. Ask yourself which one you like and will likely enjoy and go with that one. Honestly, you can't go wrong with either device.