I sometimes use those other modes. Average is good for measuring the pulse amplitude at the output of an RF detector (and for measuring other signals that have a lot a random noise on top of them). The baseline noise also rides on the top of the pulse, making measurement of the pulse amplitude tricky. Averaging averages out the random noise, leaving a clean top.
Peak mode is what I know as envelope mode (maybe they are not the same?) whereby the trace data is accumulated from trace to trace and the only peak amplitude is displayed. This can sometimes catch glitches that would otherwise be hard to see.