The following is directed at the basic scenario of a two channel oscilloscope...
At the fundamental level, the dual beam oscilloscope had a distinct benefit over and above other analogue dual trace oscilloscopes: being able to display two full traces at the same time.
I use this phrase "same time" very deliberately.
In an "ordinary" analogue scope, there is one beam - and when there are two traces, this one beam has to do one of two things:
1. Sweep out trace 1 from one side of the screen to the other and then sweep out trace 2 from one side of the screen to the other. The word used to describe this is "Alternate".
-or-
2. Display part of trace 1 and then quickly switch over and display a part of trace 2 - and continue to switch back and forth as the beam moves from one side of the screen to the other. The word used to describe this is "Chop".
"Alternate" allows a complete sweep of one signal to be made before switching to the other signal. When going fast enough, human persistence of vision (and the phosphor) has us seeing two traces on the screen at once. There is a catch, though. While it may appear that you are seeing the two signals side by side at the same time - you aren't. One trace was painted before the other. So if you are trying to chase down an issue across two signals and the relative timing is absolutely critical for correct diagnosis, you need to be very aware of the timing difference between the two traces. Also, you are only ever seeing half of each signal. It is possible to add a delay to one of the signals to compensate for the timing - but that's still going to leave you only seeing half the signal.
"Chop" allows accurate timing - but because the beam has to paint two traces, it only paints 50% of each trace and there may be significant bits of the trace that do not get displayed. It also gets difficult to Chop traces at high sweep rates.
Some CROs allow you to select Alternate or Chop while others will use Chop at slower sweep rates and Alternate at higher rates.
The dual beam CRO solved these issues by having two separate beams, controlled independently and displaying on the screen at the same time. One beam was dedicated to each channel - and when swept across the screen at the same time, the traces were complete and had no timing differences.
This was not a simple exercise - and, as you might expect, these scopes were not cheap.
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