The BC games seemed to have more soul, imo. The characters were memorable, it had that military tone, but funny and irreverent. BC2 lost it somewhat, but they made up for it with great campaigns all over the world. The destruction was awesome (collapsing 2 story buildings, or having entire maps leveled by the end which did have it's ups and downs). They felt different than the main game despite sharing some core similarities.
Definitely not the same as mainline BF, despite those games getting campaign modes. Much of it had to do with tone, but these days, that's pretty substantial, imo. It didn't take itself as seriously. I still can't remember getting those same "Battlefield Moments" from mainline games.
I also loved that the m203 was nearly standard. Only game I would actively chose smoke grenades to create screens for my teammates.
I freaking would laugh my ass off when you sneak up on a sniper in a building and place c4 on all the walls and bring down the building on them. Sooo good.