I agree with AV -- definitely the lightest option and the one you can fold fastest, and that may be two small strollers rather than one, especially a tandem, which seems really large to be lugging quickly on and off public transportation. You may find too that your four-year-old will be happiest walking as much as possible (though of course you want that stroller for the loooong walks), so I would try to find a very lightweight stroller for the older child -- a stroller you can even strap onto an adult's back much of the time to encourage the child to walk.
We went to Denmark for a week, year before last, and really enjoyed it, and so did our daughter (then 9 years old, so no stroller issues...though I've done the international stroller thing for years when she was little!). People were very child-friendly!
You may have relatives there or be from there etc., and if so, ignore the rest here, but if not...Be sure to go the Copenhagen tourist office (across from the Tivoli amusement park, you can't miss either one) and buy the "Copenhagen card" available to tourists; it seems like a lot up front but actually saves you tons of money on fares, even train fares to other cities, and on museum admissions, Tivoli repeat admissions, etc. Check out whether you think it will save you money; if you plan to hit many museums it surely will. Also, be aware that the currency exchange rate over in Scandinavia is very bad for Americans. Things are extremely expensive, including food, and in Denmark we found the local restaurant food, though tasty, was very meat- and starch-heavy and many vegetables came either pickled or in sauces -- none of which worked well for any of us. So get to a local supermarket and take advantage of it. (And be sure to take your 4-year-old to Tivoli! It's great fun!)