You can't go "wrong" with either one, as both have more than enough to keep you busy for a weekend. I'd say that as far as "sightseeing" goes, Amsterdam has a greater variety. Many of Oslo's sights relate to their maritime history (whether Vikings or the Kon Tiki). Both cities have WWII Resistance Museums, both interesting. Of course if you want to see Munch, then go to Oslo (I found the Munch Museum very interesting, particularly the pieces that weren't The Scream so I hadn't seen them before). And if you are drawn to Van Gogh or Rembrandt, then go to Amsterdam.
I too was concerned that so many came back from Amsterdam only talking about sex and drugs. However, I partook of neither of these myself, and didn't have any problem filling my days.
In your situation, I'd look at Rick's videos for both places, and see which one calls to you more. Here's Amsterdam from 2014: http://www.ricksteves.com/watch-read-listen/video/tv-show/season-8/amsterdam
and here's Oslo from 2010: http://www.ricksteves.com/watch-read-listen/video/tv-show/oslo
I'd also probably go with Oslo because it's easier to splice Amsterdam into a future trip, while Oslo is a geographic outlier. Also, Oslo's period of "good" weather is much shorter; if your visit coincides with it, take advantage.
However, while I wouldn't call Amsterdam "cheap," don't underestimate the expense of Oslo. It's certainly the only place in Europe where I actively sought out hotdogs from the 7-11 type places for dinner, just to save money. If you do go, consider the Oslo Card, which in 2003 cost me $50 for 3 days, but which I used for $75 worth of transit and attractions. If you can get Rick's Scandinavia or Norway books, they have very good money-saving tips for this very expensive place.