Sorry to be a neghead but I found these scope noise videos to be more annoying and misleading than anything.
I'm not even sure what the goal of the video is but the noise performance of a scope is set by the noise performance of the front end and the bandwidth. So I can't see how you can compare the traces just by setting the scope to the same settings and then making any claim about analogue vs digital.
If you want to show the differences between analogue and digital scopes wrt how they deal with noise (on the display) then why not deliberately inject a known noise source into the scope? This would provide more control over the comparison.
I have a wideband high level noise source here that goes out to 180MHz but I can also band limit it with external filters. If I do this with an old analogue scope I can see the Gaussian distribution of the noise really easily. I only have a crude old TDS2012 DSO here to compare with but it is just horrible to look at when looking at noise. The analogue scope is far more informative.
The Agilent scope trace in your video looks (cosmetically) horrible too when displaying noise. I'm not experienced enough with high end DSOs to say which is better (analogue or digital) but my TDS2012 is woeful at displaying noise because it can't show intensity gradation like my analogue scope can. I know the modern DSOs can show gradation but I've not tried injecting wideband noise into one yet.
Note: If you inject a very wideband noise source into an analogue scope the trace looks quite pretty because it shows a really clean 'fogging' effect and the fog slowly clears as you move away from the centre of the trace (as expected). It would be interesting to see how a decent DSO would cope.
We have some Tek 4000 series scopes at work I can try this on. Also we have some 6000 series Agilent scopes to compare how the trace looks.
Note: Noise can be your friend too which is why I have various noise sources here and I much prefer to look at noise on my old Tek 465 compared to the rather crude (and technically limited) TDS2012