Tracks recorded: definitely not, any DAW at with least 24-bit bit-depth records exactly the same thing.
Straight mixdowns without any EQ/comp/etc: There shouldn’t any differences between any 32-bit DAWs. “Audio engine” is just pure math. It can be done the right way or can be completely flawed (which I believe none of the modern DAWs are).
Further processing (with EQs/compressors/other plugins): there may be difference, because processing algorithms may be updated. IIRC there was an update on Cubase EQs SX3->CB4.