I have a Sound Devices 722. I use similar battery packs as your second link. I bought them on eBay as well. They work just fine, and last me half a day or more while providing phantom power to two channels. I carry around three. It is easy to swap them in the field so I haven’t yet had to cross the threshold of needing to invest in a much more expensive NP system when these are so cheap.
It’s possible the B&H one may last longer or carry more charge. Sometimes shady sellers will market higher capacities than the unit supplies. I personally haven’t had a problem with eBay batteries and for the substantial difference in price it’s worth it. I still prefer them to spending hundreds on an NP system.
i also have an external charger similar to (but not the same as) the one you share and I find it charges faster than charging the same battery via the 722.
Like Paul, I’ve got several of those batteries. You don’t necessarily need to buy those marketed specifically for Sound Devices, pretty much any Sony L-type battery will work. Unlike, Paul, I HAVE invested in an NP system with battery distribution. I use it to power both my 744t and a USBPre 2 to drive channels 3&4 on the 744. It does make my life a little simpler, and I usually have an L-type battery connected to the 744 anyways. It’s the back up battery. So if the NP battery bottoms out, the 744 automatically switches over to the L-type.