Sony PCM A10 if you can budget it.
Internal battery and memory (Recorded 2 shows easy but didnt want to push a third, 15 gb internal memory)
Much smaller footprint
Phone App
The deal-breaker about the Sony PCM A10 for me is the internal battery. I still have a fully functional Zoom H1 from 13 years ago, and by now I don't expect it to ever kick the bucket. 1 AA battery lasts nearly 10 hours. With internal batteries, you know the device is going to become unusable sooner or later, and it's a hassle to replace it (if you can at all).
The A10 does (I believe) have cleaner gain than the Zoom H1 for most of its gain range. But the H1 has a very sweet spot at +13 dB gain (lvl 37), where the it's actually slightly better than a lot of portable recorders (Roland R-05, Sony M10, Sony A10). If that's enough gain for what you're recording, that's excellent. But the CA-11s are not very sensitive mics, so you often do need more gain.
This is a well-amplified acoustic performance I recorded with my CA-11s straight into the Zoom H1 at +13 dB gain:
https://archive.org/details/cmw2022-12-10/10+Half+a+Life.flacHad to normalise by +20dB or so, but it sounds very clear to me. No perceptible noise. The low voltage PiP of the Zoom H1 was enough for the mics not to distort.
But for quieter acoustic performances, the Zoom H1 does not provide enough clean gain. You definitely need an external pre-amp or you end up with a very noisy recording.
And for louder performances than the one above, I would not risk running the CA-11s on the device's PiP alone. You might get lucky, but they might also distort.
Anyway, I hear the Zoom H1essential uses the same (or similar) preamp as the Zoom H1 and H1n, so that's why I'm sharing my experiences with the H1. You don't need to worry about gain staging with 32-bit float, but that doesn't mean that it will perform well if you provide it a weak signal straight from the mics. An external preamp would probably be useful then (or more sensitive mics). And for very loud music, you still have to worry about the power you're providing to the mics. You won't need a preamp, but a battery box is advisable.
So I'd say the A10 would definitely be better than the Zoom H1essential if you're recording those quiet acoustic shows without a preamp or battery box. It is capable of providing higher levels of clean gain. For shows like the one I linked to above, both would perform equally well without a preamp or battery box. And for very loud shows, a battery box would be advisable for both.
Imho the price difference between the A10 and the H1essential is not worth it, specially considering the internal battery (admittedly a pet peeve of mine). Get the Zoom H1essential and any Church Audio preamp for power and extra gain for those quiet shows (STC-9000, 9100, 9200, it doesn't matter, but one with an attenuation pot makes it a lot more versatile), and you're good to go. With the A10 you might be able to get away with only a battery box for all those types of shows, BUT the Church preamp would provide cleaner gain anyway, and it's not much larger than a battery box.