replacing diode connected BJTs by simple diodes in a current mirror circuit
"Diode connected" BJT actually is not so simple. It works in active mode actually and the collector current is a function of the base voltage. 

Side note: It is not very widely known, but the collector current of the BJT actually depends not on base current, but on the voltage across BE junction.

For the proper work of the current mirror the two transistors must be as equal as possible, so that is why it is not a good idea to replace one of them with diode.

Nevertheless, some simple discrete components schematic can use diodes, but only if there is some current negative feedback, as in the below schematic. But even there, using BJT is much better.







simulate this circuit &ndash; Schematic created using CircuitLab