At first glance, it might seem that Emmental (more familiar in the United States as Swiss) and Havarti cheeses are extremely similar. Both have the relatively unusual trait of having holes. They are even somewhat similar in colour. Beyond these superficial similarities, however, these two cheese are in fact extremely different.
Emmental, as you probably guessed from the introduction, is made in Switzerland. You may be more familiar with Emmental as "Swiss cheese"; it is one of several varieties that falls under this name in the United States. Havarti, on the other hand, is native to Denmark.
Havarti cheese has a fairly mild flavour similar to that of Monterey jack cheese when it is young. This flavour grows sharper as the cheese ages, and a well-aged Havarti cheese can be extremely sharp. Emmental is consistently mild and almost sweet.
Emmental cheese generally has perfectly round, smooth holes that can range from pea-sized all the way up to the size of a golf ball. Havarti, on the other hand, often has more holes -- but they are generally very small (about the size of a grain of wheat) and tend to be odd, lumpy shapes rather than round. Some varieties of Havarti do not have holes at all.
Havarti cheese is soft, creamy and sometimes bordering on crumbly thanks to its small holes. Emmental cheese, on the other hand, is very firm and almost springy; its texture is more like that of mozzarella.
Authentic Emmental from Switzerland tends to be a darker yellow than the Swiss cheese commonly sold in the Unted States. Havarti, on the other hand, is consistently a pale golden yellow colour.