All details about some quantization effects are totally unimportant.
The large difference is that basically what is called a "digital oscilloscope" today is a storage oscilloscope, and very good at said storage features.
While analog storage oscilloscopes exist, they are way more limited in this "storage", and most analog scopes beginners buy are not storage oscilloscopes at all.
The big difference here is, a storage oscilloscope can capture and store a waveform, for example, to record one incident, be it a digital communication packet, or a non-repetitive analog phenomenon like someone shouting an obscenity at a microphone, or recording an earthquake. You can record quite long observations, then zoom in and out, scroll it...
Analog oscilloscopes are pretty good to observe repetitive signals, for example to look at how an amplifier works when you can feed the amplifier with a repetitive signal from a Function Generator. Or to look at the triangle wave an fixed-frequency PWM SMPS generates under steady conditions...
But the big difference is, they are different instruments altogether, a digital storage oscilloscope can do so many more things an analog scope is completely unsuitable for. Especially nowadays almost every beginner wants to do something with an Arduino or similar at some point, and needs to look at UART or SPI or just GPIO. Analog scope is nearly useless for this. So you would need two scopes --
except that you won't, because the reverse is only true if very small details are important (and they usually aren't). Even a remotely modern digital storage oscilloscope can replace an analog one in 99.9999% of cases, although maybe it sometimes happens that you do have a really high BW repetitive signal and can't afford to buy an expensive 1GHz digital scope but happen to find a good deal of an used analog top performer. But I doubt it, the best analog scopes have already found their homes.