The battery is just storage. They're all the same voltage (at least the ones you'll be choosing from are), some just have higher capacity in the starting amps, and reserve departments than others.
The alternator on the Explorer is quite capable of working with any battery. Most limitations are based on the size available in the chassis, or in the old days, cost.
At least I assume it was cost. When you have a full size truck with a battery area half again larger than the battery that it originally came with, it certainly was not size that was the limiting factor.
And why most of us have long since put much larger, much more powerful and much longer warranty batteries in our trucks and Broncos.
So I say you're only limited by the physical size of the area you can mount the battery, and not by the original donor vehicle of the engine.
As said, use the largest you want and can fit. And accompany that by larger gauge cables to suit it's new use. If you're going off-road adventurin' with it, up-size to something like 2ga instead of 6ga that originally came with the Bronco and the Explorer.
And keep a body ground, like Ford did on both vehicles as well.
Paul