I take this here because for more polite I do not want smudge royal R&S thread for this.
Just for compare, (previous detail image from R&S @agdr
Same settings (afaik)
Around same ballpark (note BW diffeerence R&S 300MHz / Sig measured BW around 200MHz, nameplate BW 100MHz)
Noise comparisons have to use the same analog bandwidth, same memory depth, same sample rate, and same update rate, otherwise they are not apples-apples.
1. I told, using my whole experience and knowledge, They are "around same ballpark" and I stay ground under my legs behind this until real evidence about anything else.
Of course this answer also include knowledge how different these scopes are - just in very different performance class and in very different price class. There is not from me ANY even single doubt that R&S is higher class scope and this was not reason. There was also not reason to "compete" with R&S using just Siglent. Whole reason was that I can see there images where was enormous noise visible on the R&S screen in first phase and knowing R&S it feels very strange. Also there was shown that there was used quite good signal generator. After then I want show that even simple and cheap Siglent with even Siglent function generator have lot of less noise - so there must be something wrong.
After then, later, I realize that this some signal image enormous noise was from really noisy signal generator. (even in case there was used 60dB attenuation. (Also I use - 60dB attenuator).
After then I can see there was scope base noise images without signal.
There was averaging and so on but one trace what show quite low noise also without any trics, exept that trace was dimmed so that peak values nearly invisible and eye may think this more clearly visible trace was including peak values. But after change image Gamma It was clear that peaks was just nearly hidden if look fast this image. There was R&S measurements on but very very pity, only peak (900uV)
After then Dave throwing this a simple answer.
"Noise comparisons have to use the same analog bandwidth"No. This is for him who have low experience and unable to evaluate and calculate the aid with the assessment.
How much BW itself affect. And here we talk mostly random noise.
Everyone who do anything with signals know this: 10 log (BW1/BW2)
If compare 100MHz and 1000MHz BW random noise there is around 10dB difference.
Between 100MHz and 300MHz there is around 4.8dB difference. (if this and that and those things are same and so on)
But in practice, (I do not say just this R&S) many times 100MHz scope analog BW is well over 150MHz, in this case around 180MHz. Bit I doubt that R&S BW is not 3 times more. Perhaps 2 - 2.5x.
If it is 2.5x then 4dB and if 2 then 3dB
Now, R&S 900uV peak. Siglent ~600uV. Difference around 3.5dB. (peaks. So do not put too much weight for this!)
Siglent RMS we know. Roughly around 64uV mean with 10uV SD.
"same memory depth, same sample rate, and same update rate"Of course, when we talk random "white noise" peak values.
This is why in my example there is RMS and not only peak.
But if peak alone.
Update rate do not mean. Measurements are made from single acquisition data, not from screen pixels.
Visual trace fatness may rise with fast update rate. But, when intensity gradation works well, visually it also give image about noise distribution (situation here is terrible if not intensity gradation). Both scopes show it clearly. And if have experience it can very easy say they are Roughly around same ball park. Also in both can see not only only one or two highest peaks. If look carefully these images can get good image about noise distribution.
On Siglent screen width there is 280000 samples. Every frame have visible not only single shot but around 60 acquisitions so around 16.8 Msamples mapped and visible on the screen. So there is well enough also for peaks.
I do not know how much data there is in R&S screen. But I doubt that not so much more, more I think less.
My estimate was that this do not make big difference and not prevent me with my experience to make decision "Roughly around same ballpark"
For make more comparative measurements it is very important to use noise RMS. (This is why I also show it there)
For visual image compare need be really careful if acquisition and collected data is not enough comparable.
If we use peak values, it need think bit more deeply how comparable measurements are if they do not have same amount of data. Samplerate rise amount of data but.... But it need note that also this is not so trivial how it affect. Higher samplerate generated more data may even have adverse effect. If we have 1MHz BW and samplerate say example 10MSa/s and we collect 10M ssample data. Then we use 10Gsa/s for this 1MHz BW. And we take sequential 10Msample. Now we have same amount of data. But from 1000 times less time gap. Probability for get highest peaks is less! (note Samplefrequency/BW)
Of course also need take to account that random white noise is only part of truth in practice.
Also need take care that if scope is example 500MHz it is well possible that without selectable BW rejection aand also in some scopes most sensitive vertical setting is perhaps not with full resolution (this may rise or hide some noise) there still may be less BW for most sensitive V/div settings. In Siglent SDS1kX 100MHz even 500uV/dif is full resolution and full BW.