The Vgs of the two transistors are the same at the same current, only if base currents are the also the same.
If the control transistor is not diode-connected than all the current goes through the base-emitter junction, which changes Vbe due to the base-emitter resistance as compared to the slave transistor, where most of the current flows from collector to emitter and the base current equals the collector current divided by the transistor current gain.
This means the currents will no longer be matched as is desired for a good current-mirror.