From your OP it's not clear whether it's moving generally or moving to Copenhagen that you are worrying about. My twopenny worth:
I moved to Copenhagen from Scotland 3 years ago, we thought it'd be for three years (for tax reasons) but have decided to stay at least another 2 and probably 3 years as it is a good place for us right now. After that it will definitely be time to be leaving.
Pros:
i) Jobs - we both have interesting challenging, worthwhile jobs with colleagues we like and for a decent level of pay. This was the major factor in coming here.
ii) The city - Copenhagen is pretty small really (more like Edinburgh than London) it's safe, clean, organised, efficient, culturally interesting, family friendly, vibrant, there's nice bars and restaurants and plenty of entertainment. The social provision is astonishing, childcare etc is easily available and affordable. It's worth living as close to the city as possible to take advantage of it all.
iii) Work - life balance is amazing. I have never worked so few hours and the pay levels out to the cost of living so don't be too worried about costs, especially as so much of the social care provided by the state is highly subsidised.
iv)Summer - it's hot, dry and reliable (well in comparison to Scotland - though the locals will tell you different - it all depends on your point of view!). Cycling round Copenhagen and indeed the rest of Denmark is wonderful in Summer, we have a very outside kind of life which is pleasant
v) The people are friendly, most speak some english (though I do recommend learning Danish to help you integrate more) and are generally well educated and interested in meeting new people.
vi) Danish is relatively easy to learn for english speakers to read, though speaking and listening are always tricky.
Cons:
i) It's damn flat. Denmark may just be the most (visually) boring country in the world. I really miss topography and I absolutely miss the kind of outdoors lifestyle I had in scotland. Although saying that, if you're interested in sailing, there's plenty of that, though the West Coast of Scotland it ain't. Southern Sweden is close and a bit more interesting but, though you could consider Copenhagen a base to explore Scandinavia from, you'll always be travelling a long way to get to the really interesting bits. (Norway is an overnight ferry away for instance). OTOH once you've mastered Danish you'll understand the other Scandinavian languages too.
ii) Most socialising is done within the family so it can be hard to get to know Danes well. I have some very good Danish friends here, but mostly socialise with other expats (from all over the world not necessarily the UK). There is no real pub culture or after work going out culture.
iii) Winter is very long, colder (but drier) than Scotland and extremely grey. It's much more depressing than in Scotland (see con 1 too) because it's a kind of non-weather, the clouds come in in November and leave in March.
iv) The Danish language might just be the ugliest language in Europe and I certainly don't want my children growing up being more comfortable in Danish than any other language!
So, although I've thoroughly enjoyed living here and really feel I've made the most of it, when the 5 or 6 years are finally up we'll be heading onwards, possiby back to Scotland, or maybe on to Norway, I would like to get back to nature, but I have to admit, the advantages of living in a Scandinavian society are not to be underestimated.