In my memory Doom II is just "more Doom" but there's quite a bit of difference between the two despite running on the same engine. Doom II's inclusion of the Super Shotgun and the new enemies both do a lot to change encounters, and the map design style is much more open and puzzle-y than the first game.

The maps for Doom II feels a bit more abstract and don't sell the setting as well as the first three episodes which tell a pretty tight and convincing story between the three (Military Base -> Hell overtaking said base -> Hell itself). It's supposed to be Earth, but it isn't especially cohesive, and the more sprawling levels aren't as fun. The final boss is also some real bullshit.

Doom II is interesting and challenging, and has a few standout maps, but is a less consistently great package than the first game, which for me is a perfect game. Still, it's built on great bones, and I'd rather have an interesting if somewhat flawed followup than just more of the same.