slope of phase error versus frequency: Theory and practice for gain of 1, should be twice that compared to gain of 2. In other words to give the same output frequency change, requires twice the phase change. Why? Because for a fixed Delta omega, requires the same Delta vc for both cases. For a gain of 2 this requires Delta ve = Delta vc/2 and for a gain of 1, this requires Delta ve = Delta vc.
For lock range, theory says lock range is twice for gain of 2, practice is they are nearly the same limited by VCO characteristics, operating voltage.
Switching Transient The important thing in a synthesizer is the output frequency a measure of which can be seen at the control voltage. For this reason, students were expected to plot control voltage versus time. If you did not measure it, you were still expected to plot control voltage versus time. This means you look up the two requried control voltages, calculate omega_n and damping constant (not the same as before since your loop now has a divide by n in it). Then you estimate the shape of the transient from the standard error curves.
phase | .-.
error | / \
| / \ . __
`'
----------------
time
Divider| --------------
Control| | |
|-- ------------
-----------------------------
control| .- . -------.
voltage| .' .
|--' ..--------
------------------------------
time