The input ranges are probably not far apart. Very likely the 600uA of the Siglent is the full range on the most sensitive range, while the specifications of the Brymen state the resolution.
I have also been looking at bench top DMM's but I find it very annoying that they almost all come in very deep cabinets, and I have no room for that. In the "lower cost" range there are also handheld DMM's disguised as benchtop DMM's, but if it's still a disguised handheld DMM you might as well buy a real handheld meter. And therefore my main interest is also to this Brymen.
The Brymen's have a weird, but documented communciation protocol They basically send the LCD segments over the optically isolated connection in RS232 format.
There are some handheld DMM's with internal Bluetooth. Some Chinese meters, some Agilent meters have it, and I think also the 121GW.
Dave's 121GW also has a uSD socket, so it can log continuously until the bateries die.
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Also, It's always nice to have multiple meters, and it's quite easy to make a simple meter yourself with a uC, some ADC and a handful of passives, and adding a serial connection is also easy. Therefore I've got the idea to make a few simple meters (some that can only measure voltage, and others that can only measure current), then calibrate them with a Brymen (that's the best I'm willing to afford) The homebrew meters can have a much higher sampling rate, mostly dependent on the ADC you use.