It's about intensity & update rate, which gives information about things like jitter, noise, how often a glitch occurs etc. by the relative brightness of different parts of the trace. Only an expensive digital scope will give you this.
As an hobbyist, I used to have an old clunker > 30 yrs 20 Mhz analog scope with me, then upgraded to cheap 60 Mhz Chinese DSO that is not worth mentioning here, later had a good luck to secure a fully working and cheap analog beast Tek 2465B while ago. Agree with Mike above, at the trace's varying brightness, really minor glitches, micro spikes at etc that made a decent analog stands out against digital scope especially the cheap ones.
For special cases when it comes to capture single shot or non repetitive signal, digital simply beats analog out of the water, no contest here, and when it times you need this, analog scope really just can not help you.
I'm lucky in the sense that I have access to several analog scopes ranging from 25 to 350MHz, .......
Don't forget Alan, that 350 Mhz beast of yours has the unique feature that the crt tube can sweep faster than speed of light.
![Wink ;)](https://www.eevblog.com/forum/Smileys/default/xwink.gif.pagespeed.ic.cldandycH0.png)
IMO, in enthusiast/hobbyist world which usually have limited budget, a combination of "properly working" old analog + cheap DSO is the best combination you could get and yields the biggest bang for the money.
The biggest challenge and major problem is getting a cheap + "still properly working" old analog scope.
![Huh? ???](https://www.eevblog.com/forum/Smileys/default/xhuh.gif.pagespeed.ic.6Nvt7O8a11.png)