There is a critical gap between the sensibilities of Doom/Quake/Duke and Painkiller/Serious Sam: level flow. The latter camp is in varying degrees a series of rooms you get locked into as enemies spawn in waves. The former involves navigating a highly varied environment as you attract the attention of pre-existing enemies.
Sure, on the avatar scale, they play at a similar level. The environments are what really set the earlier generation apart, and in that respect very little approaches that sort of design.
Painkiller sometimes does that, but other times it gives you levels like Docks, where as much vertical traversal is expected as horizontal: https://www.youtube.com/watch?v=5-0yJ2V41Jk
I'll happily agree that Painkiller has some more variation then SS, but on the whole it's much more focused with wave-based arenas. This isn't a knock against Painkiller at all, it's a favorite of mine - yet it's still a bit inaccurate to regard it as classical level design.
Sure, on the avatar scale, they play at a similar level. The environments are what really set the earlier generation apart, and in that respect very little approaches that sort of design.