I don’t understand the ‘vs.’ in the title.

What do backing tracks have to do with sidechain compression?

Probably the first use of sidechain compression that everyone knows is automatic volume reduction of program audio when a radio announcer is speaking. Usually using a very long release on the compressor.

What you describe can certainly be done with a DAW with a modular signal path like Tracktion.

Split the vocal channel and send the split to an EQ that passes the frequencies you want to cut in the other track. Take the output of that EQ as the ‘key’ for the sidechain. The signal that you want to ‘cut’ should also be split. One side, let it go to the mix buss, the other side you send through the sidechain. On the output of the sidechain put an EQ on of the frequencies to cut on command.

See how this works?

It’s just eq’ed sidechain