There are a lot of differences, but I think two economic factors help it in Denmark (ok, I ended up writing mostly about the 1st):

1.

If you think of the country of Denmark itself as a large corporation of sorts, its goal in the international market is to go high-end. The workforce is too high-wage to compete on regular manufacturing, cheap worldwide food prices mean the traditionally important agriculture sector now contributes a mere 5% of GDP, and it doesn't have the oil of Norway. So it's the only choice really: to be a leader in high-skill services, R&D, and high-end manufacturing.

[This paragraph is an aside:] This view underpins lots of stuff that goes on in both the governmental and industrial sectors. As one example, there is a goal that within 20 years, 100% of Danes will earn a college degree, and 50% (!) will go on to get a masters degree, in order to position the country's workforce as highly educated, almost like a 6-million-strong consulting shop. They're willing to pay for it, too: there is no tuition, and students receive a modest living stipend. The similarities to a company are surprisingly deep, e.g. the unemployment program is even run a lot like an HR department, viewing un/underemployed people quite literally as potential "human resources" who can be used to plug labor shortages elsewhere, with the right matchmaking and training. On the services side, it's been reasonably successful, though honestly in part due to good fortune in making the transition: Carlsberg and Maersk are huge parts of the Danish economy, despite the fact that actually brewing beer and building/sailing ships are long-gone as mainstays of the economy. They managed to transition into having Danes as the managerial class of global companies when the manufacturing jobs moved elsewhere. It's not hard to imagine an alternate-history scenario where Copenhagen ends up as a poor post-industrial city full of derelict shipyards, instead of a rich post-industrial city full of loft conversions in former shipyards.

Wind energy has been a lynchpin of the R&D and high-end manufacturing part of the strategy for a while now, from both the public and private sides. Denmark's location makes wind a reasonably good choice among the various things you might want to pursue in the energy sector (I wouldn't recommend a solar-based strategy here). And so it's become not only big domestically, but a major export business. Denmark-based Vestas has long been the #1 worldwide wind-turbine manufacturer, one of the few global "#1s" in a country of 6 million. You can aso see it in the "branding strategy" of both the government (http://denmark.dk/en/green-living/wind-energy/) and the industrial sector (http://www.windpower.org/en/). And it spills into other things, e.g. "smart grids" to manage the variable load of wind energy are now a big R&D initiative at the university I'm at, with hopes that Denmark will become a leader in smart-grid tech too.

So what I'm getting at is: domestic wind farms are rather multi-purpose. They do serve a primary function of actually generating energy. But they also serve a secondary function of building up the wind-export sector, and another secondary function of building up a certain image that Denmark wants to project, of a 21st-century R&D and high-end manufacturing hub, and of generally being "ahead".

2.

Many of the wind farms are organized as consumer cooperatives, so have broad-based ownership, which produces built-in supporters. For example, the farm offshore of the island of Amager (just east of Copenhagen) is co-owned 50% by the municipality, and 50% by a cooperative with 10,000 members.