There are times when you want to look at signals with quite high frequency components, whilst using a very long time/cm setting.
The classic case is looking at analog video at field rate.
DSOs with very small memories commonly reduce the sampling rate savagely at such settings, to the point where the required display is lost in a forest of aliasing.
The early DSOs ( & some currently available really cheap ones) cannot even display analog video accurately at line rate.
OK, analog video is no more, but try looking for 50/60Hz "hum" on any pulse train with HF components!
It took a while for hardware integration and performance to reach the point where real time histograms as in DPOs (Digital Phosphor Oscilloscopes) or large sample memories were feasible. Even today the display quality of a DSO capable of displaying an analog video signal is poor.
Personally I prefer the short record length and high acquisition rate of a DPO. See below about waveform acquisition rate.
The early digitising scopes were awful to use, except in some circumstances. Hence the correct statement that analogue scopes were usually better.
I would say the boundary between good and useless shifted with the Tektronix 2230/2232 which were the first DSOs to support peak detection. They lacked index graded displays but at least they could capture the envelope of a single on every acquisition.
For digital signals, the only thing that matters is the transition speed, tr; the period is completely and utterly irrelevant. The usual rule-of-thumb is that the signal bandwidth is 0.35/tr. There are a few nuances, but at this level they can be ignored.
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Hence if you have, say, an Arduino which changes the output once per hour, and it takes 5ns to go from high to low, then the maximum bandwith in the signal is 70MHz (i.e. 0.35/5e-9) - and you scope needs to be faster than that.
This cannot be stressed enough; instead of thinking in terms of bandwidth, think in terms of transition time and the 0.35 rule:
20MHz 17.5 High Voltage CMOS
50MHz 7.0ns Standard and LS TTL and HCMOS
100MHz 3.5ns Fast TTL
200MHz 1.75ns ECL
Probing above 100MHz becomes increasingly difficult. 200MHz is feasible for general troubleshooting with the shortest ground lead but higher will require a expensive active probes, low-z probes, or probe tip adapters. If you are not prepared to deal with these, then avoid instruments above 200MHz unless you plan on only using coaxial cables.
Hobbyists frequently unwittingly create the conditions in which there are infrequent random failures or failures that take a long time to become apparent. Classic examples: failing to observe data hold times (setup times are comparatively easy), incorrect termination leading to voltage spikes which slowly damage receiver inputs, non-monotonic transitions on clock lines, ground bounce, and several others.
If present, those signal integrity problems probably won't be seen on a 20MHz scope. So when their design doesn't work as expected, people will start looking in the wrong place. Seen that far too many times!
This is the place where waveform acquisition rate matters. A real time DSO display only requires 30fps but might take days to catch an elusive metastable event. In practice hobbyists will have to live with whatever they can find which is pretty good today compared to just a couple decades ago even on basic instruments.
As far as the number of channels, almost all two channel instruments include a trigger input somewhat relaxing the requirement for a 4 channel oscilloscope. But if you want to decode 3 and 4 wire serial buses like SPI, 4 channels is a great improvement. Some low cost two channel instruments (HP? R&S?) can now use their trigger input as a third channel for SPI decoding.