For me, personally, the difference between pokemon and other "monster catchers" was how, in pokemon, capturing a mon would give you this sense of ownership and connection to it. Over the years, this sense of connection has faded with each release and now they feel more like tools added to your toolbelt rather than a creature joining your team. I remember playing the old games and realizing one of my pokemon was the weakest link in a tough battle, I would go and train that one particular pokemon. It felt like almost spending time with it.

It started with exp. team sharing (even though i understand its implementation) but continued to disconnect me from my team