I find Duke Nukem 2 to be too "busy", I've only just gone through the first few levels but I think I prefer Duke Nukem 1 more. I also think the characters are too big and there isn't enough screen to work out what is going on around me. I grew up on Duke Nukem 1 and never played Duke Nukem 2, so maybe that is a factor.

Which do you prefer and why?

Difficult question. I like both games but for different reasons.
For example, Duke Nukem 2 have Sound Blaster effects and AdLib music. First Duke Nukem only have PC Speaker sounds and no music.

In the end of they day, I find myself switching between the two games very often.

Definitely one for me, one of the first platforms I played and it holds a special place in my heart.
2 is still fantastic however :)

I like them both, but I think I like Douk 2 the best in the entire series, that's including Douk3D, So call me a crazy nostalgiagoggled weirdo. And I'll admit to that, it's mostly due to nostalgia.

Definitely the first one! 2 is really a boring generic shooter. Not even the SB music and sound effects can save it.

I never played either of them back in the day when they were released, so was able to approach both objectively a couple of years ago.

I loved the first game straight away. The sprawling level design was mostly great, except for a few parts where getting hit seems inevitable. I liked the art-style, sound effects and tight controls on keyboard.
Then I tried the second game and honestly wasn't too keen on it at first. It had its own merits such as more detailed graphics and there was the music and everything. Thing is, it was just so different. It was more of a run and gun side-scroller than the platformer the first one was. Nothing wrong with that, but it meant it wasn't a clear-cut case of more-of-the-same-but-better, nor was it a case of different and better. IMO, it was different, but had more flaws in its design than the first.

The level design at first felt fairly linear and cramped. I didn't like the scrolling and about the detailed graphics: htown1980, you took the words out of my mouth there when you described the second one as "too busy". Those were my thoughts on DN 2 on first playing it (I still think that, actually).

All that said though, DN 2 did grow on me a bit. Yes there are faults:
- Art style too busy and cluttered,
- Jerky scrolling with limited vision; the view is too 'zoomed in' / everything including Duke is too big onscreen and combined with the way the scrolling works it results in instances where it's very difficult to react in time if you haven't learned what's about to appear from off-screen.

So in the end, I think I still prefer the first one because it's 'cleaner' and more focused, with tighter design. It's less of an arcade mashup like the sequel and knows what it is, sticks to that and is good at it.
Taken as the different game that the sequel is though, and when judged in its own right, for me Duke 2 is flawed but still a lot of fun (if a bit trial and error).