No experience with automotive signals, so I can't help you with that. An analog scope should show every firing if the repetition rate is high enough to show a stable signal (more than a few Hertz), although there is a limit to how fast it can refresh. A digital storage oscilloscope, aka. digital real time oscilloscope (to distinguish it from the older digital sampling oscilloscope), can do the same. On the cheaper models, the refresh rate is much lower however. Usually tens to hundreds of waveforms per second for the low end up to a million waveforms per second for the Agilent DSO-X 3000 series. But even ten waveforms per second should give you a reasonably responsive picture if the signal is stable. Some people like those analog tube scopes because of the sharp trace which gives it more vertical resolution than an 8-bit DSO with 1 bit of quantization noise.
There were analog storage oscilloscopes that could capture a signal and store it on the CRT by electrostatic means, but these are ancient relics, I don't see any reason to use them these days unless you happen to have one around. Another tactic was to mount a camera on the scope and fire it after the signal has triggered the scope. It would take a picture right after the scope drew the signal on the CRT, and the phosphor would glow long enough for the picture to be taken.
A mixed signal oscilloscope combines analog and digital inputs. I don't see any reason to use digital inputs in your case unless the timing is controlled over the CAN bus.
There are good reasons to keep both a digital and an analog scope around, and some scopes are better suited for certain tasks (eg. portability, high bandwidth or very sensitive and low noise), but I would guess that most people keeping many scopes around do this because they like them, not because they need all of them.