RCA made the BA43 to replace the earlier BA33. The BA31 and BA33 are older, and I believe they're germanium based. They both have built-in power supplies too. The 31 is much smaller, only about 1.5" wide. It's pretty much intended as a mike preamp or line amp. The BA33 is essentially the same circuit, but it has an input attenuator and it has a much more robust output. It's intended as a program amplifier. Back in the days when this was state-of-the-art broadcast gear, the program amps had to have tons of headroom because the signal feeding the transmitter got pushed into much higher voltage levels, and remember this was in the days of 600 ohm terminations. In other words, the BA33 was a little power amp. The BA43 is the same deal, but it's a little newer and I believe it's all silicon, though I haven't checked. In any case, these are robust preamps that can do lots of different things, most noteably serve as mike preamps. Since they have so much headroom, you can drive them pretty hard (turn up the input attenuator) and get the transformers working, and then pad the output (it'll also get you better noise performance than if you turn down the input attenuator). This headroom would also make these units very appropriate for makeup gain after (or before) a passive equalizer.
These units (BA33 and BA43) were solid-state replacements for the all-tube BA23, which did pretty much the same thing. The tube BA21 was the same size as the BA31 but didn't have an internal power supply. I've never seen anything about a BA41, and I don't think such a thing was ever built.