Hey there, and welcome.
I have noticed the games play differently. I've finished Serious Sam classics and Serious Sam 3 on Serious mode, and both take a whole different gameplay approach. Serious Sam classic is more about learning the enemy: Movement, attack patterns, dodging, how much ammo you have to spend, etc. And then with that knowledge you have to manage fights. Serious Sam 3 has a whole different layer of depth with reloading, sprinting and iron sights. But it feels like it loses enemy complexity, enemies are more straightforward but are way harder to dodge.
So in short, the classic games to me feel like reflexes and knowing the enemy while Serious Sam 3 feels more like being good at dodging and more trial-and-error. I really had to get used to the high amount of hitscan enemies, and despite what the tagline says, some parts require you to take a more cautious approach thanks to this.