The obvious thing is you need to use two of the common first orders to get the same response as a single second order. When you think of second order all-passes you need to bundle pairs of first orders.

The total phase shift has to do with the total number of stages. However, where the notches end-up depends on the shape of the phase response.

Second order stages are not all the same. When you have a second order stage you get an extra parameter you can control, the Q. You can actually choose the Q with two first order stages by using different caps in each stage, for example like the univibe. When the caps are equal the Q is 0.5. When the caps are different the Q is less than 0.5. The second order circuits let you set the Q more than 0.5. That's something you can't do with a first order.

The higher the Q the quicker the phase changes from 0 to the maximum. If the phase changes quicker it will hit the notch points (where the phase is -180deg, -540deg, -720deg, -900deg) at frequencies closer together.

Here's the phase response of a low-pass filter as the Q is varied.

** You need to double the phase on the left axis to get the phase for second order all-pass. ***

http://www.analog.com/-/media/images/analog-dialogue/en/volume-41/number-4/articles/phase-relations-in-active-filters/ad41-10_17.jpg?la=enThe main thing to notice how quickly the phase changes as the Q is varied.

If you have ever removed the dry path from a phaser you will notice you hear a vibrato effect. There are no notches when you do this. So that means there's more to the sound than just notches. When you use a higher Q value the amount of pitch shift increases.

Many second order circuits don't allow you to sweep the frequencies, you need to choose the right type of second order all-pass.