No, the most apparent difference is what different compressors SOUND like.
Yes, there's a passion for 'retro' gear in some parts of the recording world.
If 'what a 1950s Fairchild tube compressor sounds like' (minus the hum) is your definition of perfection, I expect you'll be able to detect how a digital emulation isn't QUITE identical. (Though computers have an uncomfortable habit of casually overcoming 'they'll NEVER manage THAT!' barriers.)
'It's not about the gear' becomes increasingly true as high-quality recording hardware becomes increasingly affordable and digital emulations become increasingly accurate. Good. It can be 'all about the music'.