There are many, many, many possible performance parameters to look at when deciding for a scope, and also when deciding between an analog and a digital scope. BTW, virtually all higher-end scope today are digital sampling scopes because they can be MUCH more flexible than any analog scope, and with sufficient computing power they pretty much give a real-time display (once you are at 50 frames/sec or more, your eye won't be able to see any difference).
For a hobbyist of course price is a big factor, and that makes older, used analog scope look attractive again. It really depends on what type of signal you want to look at:
- remember that for a digital sampling oscilloscope (DSO), your sample rate should be about 10x the highest signal frequency of interest, unless the scope is doing a great job at interpolation (then the sample rate can be as little as 2.5x - 3x your analog bandwidth). So if you want to look at the Picaxe's 16 MHz oscillator, you really need around 160 - 200 MSamples/sec. Most cheap USB scopes offer only 50 - 100 MSamples, some even less, which is good to maybe 5 - 10 MHz. That's where even an older analog scope comes in handy - cheap ones typically have at least 10 MHz bandwidth, and it's quite easy to pick up a 60 MHz one for little money. That said, many DSOs have an equivalent time sampling mode which provides very high effective sample resolution for repetitive signals.
- on the other hand, analog scopes are a horrible choice for looking at isolated, rare events that require single-shot capture. In times past people made do with them by taking screenshot pictures with a camera with long exposure time, or with specialized scopes that had cathode ray tubes with long afterglow. But there isn't a good reason to do this nowadays. Much better to use a DSO for that.
- same thing, analog scopes aren't very convenient for displaying slower trends as well - once your trigger rate drops below about 10 events/sec the screen becomes very flickery until you see just a small dot moving slowly across the screen for slow timebase settings.
- another place where a DSO really shines is capturing the signal BEFORE the trigger. For analog scopes the trigger typically starts the sweep, so you cannot observe what happened before or shortly after the trigger instant. Digital sampling scopes can easily implement such a "pretrigger" option, while an analog scope needs a ton of hardware (delay lines) to do that. Very important if e.g. you want to trigger on a failure event and see what lead up to it.
- DSO's are much more user-friendly when you need to do measurements on your signals - frequency, period, levels, rise and fall times, etc. Most DSO software can do that for you automatically. On an analog scope you always need to measure or count grid intervals, then multiply that by hand with the timebase or sensitivity setting - slow, tedious and error prone.
- space requirements - an old cathode ray scope is large and heavy. A USB scope is typically very small. That can be an advantage if your lab space is limited to one half of your desk
Overall, for a person on a limited budget who wants to be quite flexible my recommendation would be to get a simple but decent USB based scope for most measurements - something like 50 to 100 MSamples/sec, with maybe 50 MHz analog bandwidth and an equivalent time sampling mode. In my experience, they are more user friendly than the rock-bottom low-end Tek or Agilent scopes (which usually lack sufficient computing power for fast screen refresh rates, and often have a pretty bad noise floor, while the USB based scopes have your high-power PC or laptop at their disposal for data processing). And then in addition look for a good used old 100 MHz analog scope if you really need to look at very fast signals. If you can spend some more - between $600 and $2000 - get a decent new or used Tek, Agilent or Lecroy DSO to cover all those needs in a single box.
Wolfgang