Splitting an odd number of days between Cop and Stockholm, which should I allocate more days for?

If that is what you have I think Stockholm 4 days has more to offer than Copenhagen.
But you should do research to see what each city has to offer that you are interested in.
What sucks to me is that both are goofy expensive and you have to deal with two different currencies

You'll get better answers if you gives some information about your interests. I liked Copenhagen much more than Stockholm, and I wouldn't consider just a day there to be worthwhile. However, that's because I like architecture. - - great examples from many periods - - history - - terrific National Museum, Roskilde Viking ships, outdoor museums, and art - - Carlsberg Glyptotek and Louisiana,

@Jazz+Travels: What in particular makes them expensive? Restaurants, transportation, ect? How would they compare in expense to say, New York or Chicago? As for lodging, I looked up some AirB&B rates, which seem pretty reasonable.

@Rosalyn: I enjoy walking around and exploring on foot. Historical sites would probably be of most interest to me, as well as outdoor sightseeing and water activities, like boat tours and swimming.

I've no doubt both cities have plenty to offer, I'm just wondering which should I allocate the extra day for.

I would likely give the extra day to Copenhagen, both to be sure to include a Roskilde day trip and perhaps another day trip, and also if you might be jet-lagged upon arrival there.

@Laura - That sounds like a good idea, what is the best way to get to Roskilde from Copenhagen? If by train, should I order tickets before I arrive?

There are 5-6 trains per hour between Copenhagen and Roskilde and no need to reserve within Denmark. I'd buy tickets in the train station. Sightseeing in Roskilde is walkable from that station. The trains to/from Stockholm, however, are reserved and cheaper if booked ahead at www.sj.se.

I'm not Jazz+ Travels, but my experience is that Copenhagen and Stockholm are expensive for sit-down restaurant meals and alcohol, and that's about it. Everything else is either about the same as or less than what you'd expect to pay for the equivalent in a major US city. This includes things like informal cafe meals, street food, snacks bought from grocery stores (so there are plenty of options to keep yourself fed without venturing into the pricey restaurants), local public transportation, intercity trains, site admissions, accommodations, and small souvenirs.

When people say that Scandinavia is ridiculously expensive, I think they're either (1) judging in comparison to regions like Eastern and Southern Europe that are cheaper than the US, (2) judging based on the prices in sit-down restaurants, especially if they were unlucky enough to visit one of the places that doesn't tell you the prices before you order, or (3) judging the whole region based on prices in Norway, which (so I've heard - I've never been) really are higher than those in the neighboring countries.

Anyway, to answer your question: I don't think you'd go wrong either way. But one major difference you might want to consider is that Copenhagen's flatness and compactness make it a lot easier to explore purely on foot. Stockholm is centered on a cluster of islands, so it's more spread out by necessity. The public transportation system will efficiently whisk you among neighborhoods that, individually, are all very walkable - but it does mean you need to have slightly more of an idea of where you're going before you set out.

I stayed in Copenhagen and Stockholm for 4 nights each about a month ago and found that I could do just about everything I wanted to in 3 days. I found it very easy to walk and take public transportation around both cities, which allowed me to see everything I wanted to, with some down time. I like Copenhagen better than Stockholm but it all depends on your interests. On the last day of each trip, I took trips outside of the city. My last day in Stockholm I took a trip out to the archipelago and from Copenhagen I took a trip to a couple castles up north.

Both cities are beautiful. Enjoy your trip!

@khbuzzard and jennakalkwarf - Thank you both, your information was very helpful!

boat tours and swimming.

A vote for Copenhagen: http://www.visitcopenhagen.com/copenhagen/6-ways-conquer-copenhagens-waters

I will put in a vote for Stockholm. I spent 3 nights in both and would go back to Stockholm. Metro is very easy.