Before any of the direct drive amplification solutions were even a thing, I had the AHB2 driving the SR1a. It had enough power to drive them with authority but it sounded lifeless, flat, clinical and was ultimately returned. o my ears, a Schiit Vidar power amp did a better a job than the AHB2, and even better in dual monoblock configuration. I ultimately settled with a SPL Performer s800 power amplifier.
Then the JotR was released, I liked it for the form factor and its ability to drive the SR1a with grunt and control for such a tiny box...but it still wasn’t better than the Performer s800 power amp. The JotR sounded thin, shouty and harsh in comparison. Fast forward a few months and the HSA-1a was released, it was a massive improvement over the JotR driving the SR1a but the conventional headphone output was mediocre. The traits of the HSA-1a when compared to the JotR can be summarized as a much better treble presentation - a lot less harsh but you could replicate that at loud volumes, improved clarity, expanded soundstage, better bass definition.
RAAL-requisite went back to the drawing board and the HSA-1b became a reality, mostly based on the feedback from early adopters of the HSA-1a. The HSA-1b is the HSA-1a on steroids, it does everything better, the most noticeable improvement being the conventional headphones output.
So the short version of my answer to your question is, based on my experience and my preference, the HSA-1b will do a better job highlighting the strengths of the SR1a and will drive them to levels that I don’t believe the AHB2 would be able to.