Looking at the specs, self noise is rate 17db for the Rode, 18db for the Sennheiser and 19db for the Core, but then sensitivity is 30mV for the Rode, 31mV for the Sennheiser and 7mV for the Core - so perhaps it the extra gain needed contributing to that.
I’d love to hear an A/B/C/D test on them though (with the expensive soundfield) as specs can only say so much. I think the with the Ambeo it’s the frequency pattern of the noise - quite high pitch, that makes it feel prominent, but I’d need to record some more to be sure.