Horses for courses I suppose. I have three analogue scopes and one DSO in my home lab. The DCO gets used maybe 1% of the time, when I need the singe event/slow event/storage capabilities. For the rest of my work there (audio, tape recorders, metrology, some RF stuff) analogue scopes work better for me. At work I have the opposite, on my bench there are three DCOs and only one simple analogue scope (which I would use for a quick troubleshooting and fault finding - so not very often).
Here is my summary:
Analogue scopes
Advantages
1) Important. Telling the truth most of the time. What you see is what you get. If you can see something, it is usually there.
2) Can see things which DCOs have great difficuly in seeing. Like AM RF or a mild 25Mhz oscillation in a power amplifier on a particular part of 1kHz sinewave... .
3) Quick. Both in startup and reaction when you touch a point with the probe.
4) Usually considerably cheaper.
Disadvantages
1) Can not do what DSOs do easily (single events, precise timing, easy screenshots, quick measurements, FFT, comms etc)
DSOs
Advantages:
what their analogue counterparts can not do - see above.
Disadvantages
1) DCOs are untruthful by their nature. Unless you know beforehand what you are looking for, what is on the screen may have nothing to do with the reality. Which creates a particular problem when you are troubleshooting... . You have to check and cross-check what you see to be sure.
2) Almost useless in some situations (see above, especially if you don't know what to expect, say with RF oscillations in an analogue circuit with a slow changing signal).
3) Slow. Slow in start up, slow in operation, slow in the reaction on the probe. You get used to it, however if I need to fire a scope and do a quick fault-finding in an analogue circuit, an analogue scope saves a lot of time, in most cases I would see the problem before a DCO would finish the boot-up sequence... .
Cheers
Alex