2) Is the inability to overlay a math function on the main display a limitation only of the Rigol, or does the Siglent also have this limitation?
I don't have a Siglent to confirm, but there was one suggestion in one of previous posts that yes it can display a math trace just like a regular channel in the main window.
If this is really so, then it is a
big advantage, if you are ever going to use math to correlate a direct input trace with a math trace -- for example, monitoring an IC's input signal on channel 1 and a difference, if you don't have a differential probe, between two nodes in the output section, as an A-B math operation using channel 2 and channel 3 signals as operands (in other words, software emulation of a differential probe).
As a Rigol DHO804 owner, I can say that it creates a feeling of an undercooked prematurely released product to begin with, and of a toy, even if a very capable toy, on top of that. No it's not bad, not even close. It just really sucks that a very decent hardware has been created only to run such a crappy software.
The only reason why I bought it was that getting the Siglent here, at least at even a remotely reasonable price, was and still is not an option, whereas I could get the Rigol for $342 delivered from Aliexpress (sale + publicly available coupons). Frankly, that's about the price higher than which I would not be willing to pay for it (and that on the condition that it is hackable to DHO924 sans the hardware difference), especially now that the Siglent has been released and reviewed.
From what I have read in the respective Siglent review thread, it has its (minor) issues too, but it's a much more mature and serious product overall. Whoever designed the Siglent apparently understood the requirements and expectations of a competent user better than their counterparts at Rigol -- or maybe the latter did not care about that audience at all.
Another nice feature that I'd like to have and that is missing in Rigol, but, I believe, is present in Siglent is that the latter allows you to enter an arbitrary probe multiplier factor. Possible use cases are: 1) DIY probes made of a piece of coax and a resistor (e.g., 21:1 ratio with a 1k resistor and 50 Ohm feed-through terminator); 2) current transformers of whatever mV/A or V/mA ratio; 3) fine tuning of non-ideal 10x or whatever probes to improve amplitude measurement accuracy.
p.s. I am not sure that I would have been fully satisfied with Siglent, either. Reading reviews is one thing, actual usage is another. Take my words with a grain of salt. My critical views are amplified by the fact that I can't stand incompetency in software and UI development, especially in commercial products: do your job well or GTFO. Rigol fails this check.