mmm22: One thing that you haven't really mentioned is the bandwidth needed for your measurement. It will be a major factor in deciding on a scope.
You mentioned early-on a pulse of few nanoseconds, and that you want a "quantitative" measurement. What value are trying to quantify? Amplitude? Edge speed? Decay? Timing in relation to another signal?
For example, the TDS3032B that you mentioned is 300MHz. The Keysight EDUX1052A that you later mentioned is only 50MHz. On the latter, you'll see a pulse of only few ns as a lump. It will be greatly attenuated and with little detail. You'll at least get closer to an actual amplitude on the TDS3032B, but it will still not show you much detail.
I think if you described what you were trying to do, or at least provided an example waveform and what you were trying to accurately measure on it and how often, you might get more congruent answers from this thread's participants.