This may be anecdotal and loosely related - but in my experience the Biomek 96-channel MC is rock solid. I’d expect this performance to translate similarly to a 384 channel variety. However… The tips for biomeks have given me so many headaches (See the variety of lists here). It is entirely possible (and most likely) that the manufacturer of the 384 tips is different than mfr of 96-format tips, but it’s worth consideration for your potential new instrument; There might be external factors which may impact your pipetting accuracy greatly.
I’d also suggest reaching out to the technical teams of each instrument mfr directly and ask for the testing parameters where the volume ranges were detected. Maybe there’s some surprises, like potentially Hamilton didn’t test below 1 µL? I’d be very surprised if the STAR 384 performed worse than Tecan/Biomek - I’ve always considered their instruments very strong in the volume accuracy category.