I came from the Razr Maxx.
Battery life between the two is comparable for me, maybe just a bit better on the Maxx, but nothing to brag about.
I spend most of my time in a cell phone fringe area (Verizon), predictably the Maxx had better reception/ability to hang on to a call than the S4 does. With the Maxx I could go anywhere in my house and not drop a call. With the S4 there is a room in the center of the house where I WILL drop the call if I go in that room. So I've learned not to go there during a call...
Those are two points in favor of the Maxx, all other points are in favor of the S4. A much nicer screen, it's faster, I like Touchwiz (that said, I use a 3rd party launcher).
Overall it's a step up from the Maxx, which I don't think you'll regret.
For the record, the battery in the Maxx CAN be changed, I upgraded my Razr to a Razr Maxx, so I know it can be done, it's just not quick and easy like it 'should' be.