I had a Maxx HD and I've now had the S4 about 5 days. The battery life is pretty decent on the S4. For example, after a day at work (7 am - 5 pm), with my average usage, the Maxx HD would be down to 65-70%. The S4, with the same usage pattern over the past couple days, gets down to 50% (so far not below). I can totally live with that.
We'll see if it changes, but for now I'm satisfied with the S4. I did invest in a spare battery that I keep charged at the office in case I head some place after work where I must have a 100% completely full battery (even after topping off in the car). I'll swap before heading out and let the original charge for the next time. Haven't had to do that yet.
And the S4 feels twice as fast as the laggy Maxx HD, which certainly makes up for the battery difference.
Posted from my Galaxy Note 8.0 via Android Central App