The difference is, that to get an andelslejlighed, you have to buy an "andel", that is to say a part of the entire building, which is nessecary for living in the apartment, which is usually, but not always, cheaper pr. month than a rented flat.
So in many ways andel resembles a condominium more than a rented flat, and again, there can be problems with andels.
If you have money to buy an andel, you should seek professional assistance, loans in the building are often cheap in the beginning and become much more expensive later, so the "rent" grows much bigger, AND the andel becomes hard to sell.