Need help with correct wiring when replacing a hardwired smoke detector
You should find an installers manual for the main panel and read it thoroughly. But I will give you my thoughts below. 

First off, your black wire is connected to the positive terminal not the negative terminal according to your picture and wiring diagram.

Secondly, I am suspicious that this detector ever worked since there is no second wire connected to the power supply terminals. According to the label it takes 12 volts DC to power it and you can't do that with just one wire.

Without seeing any installers manual, I would say the black and white are 12 volts DC power and the red and blue are the common and signal wires.  

So test for voltage between the black and white wires. If you get 12 volts move the white wire to the other power supply terminal. Usually the auxiliary contacts would be for another system to be notified that the detector is in alarm. The red and blue should probably go to the ground and signal terminals and the auxiliary terminals are just that, auxiliary. Then see if the detector works. 

Notice on the backs of either detector they don't show any wires connected to the auxiliary contacts.