I don't know where you're coming from or what you're looking for, as that might make a difference.
Oslo is quite small for a European capital city -- about .5 million in the city -- but in a prettier location than Copehagen. Copenhagen has about 1.5 million, making it more like a standard European capital with more street life, night life, etc. If I compared them to American cities I'd say Oslo is like Anchorage; Copehagen is more like Portland, OR.
You can probably conquer Oslo in 2 full days with ease, leaving you a couple days to get out of the city for some time in the great outdoors. That may be better in summer, since it's likely still cool and rainy in April, but if you are aching for some Scandinavian scenery and the like, then I'd pick Oslo.
If you want a more urban experience though, I think it'd be a lot easier to entertain yourself in Copehagen for 3 or 4 days. Denmark is a lot flatter, but Copenhagen's got more going on.