Never played the first Serious Sam, but I played Serious Sam 2 (or rather, the demo) around the same time I tried Painkiller (or rather, the demo). Have to say that I preferred Painkiller, even though sending a bomb-laden parrot to blow up in the face of an alien football player or clockwork rhino is indeed tons of fun.
Painkiller just had style, and it had weapons that were really interesting combos that made you wonder why no one else had put them into games before. Using the titular Painkiller to clear out an entire hallway (either by using the ranged attack on a wall or by using the special-special attack to just chew them up) was loads of fun, as was finally mastering the art of tossing a grenade and then punting it with the stakethrower to make a makeshift rocket.
Or, heck just using the stakethrower to pin some goon to the wall.
And it even included periods where you would transform into a demonic entity who could literally shatter living enemies by just looking at them.
I've got this little itch in the back of my head that tells me I've played exactly this kind of game before... But I can't remember what it was.
Black and White is always good for a run-around, but even though that's close (throwing fireballs at villagers, picking up villagers and tossing them, picking up rocks and throwing them at villagers, throwing fireballs at rocks and then throwing the flaming rocks at villagers, teaching your creature to crap on eat villagers, the list goes on and on), it's still not quite the same thing.
Uhhm... Lemme think about this for a while... I'd really like to remember that game, because I'd like to play it too...