There are two types Islamic mortgages: Murbahah and Ijarah. They do not not charge interest to the borrower, but instead charge a rent or service fee. For all intents and purposes Islamic finance is the same as Western-style mortgages and they cost the borrower the same.
Murabahah is where the bank purchases the property from the owner, and then sells it to the buy in tiny fixed monthly increments, decreasing as time goes by. In case of non-payment, the bank cannot charge a late fee, but instead they have a large "reminder" fee that coincidently is about the same amount as western bank's late fee.
Ijarah is where the bank purchases the property from the owner and retains ownership for the entire length of the loan. They charge the buyer a tiny fixed monthly rent, decreasing as time goes by, to either occupy it and rent it out to a tenant. At the end of the loan term, the bank transfer the property to the buyer for free.
With Islamic financing, everybody wins. People get to purchase a property on leverage while still remaining Shariah compliant. Westerners might as well take advantage of an Islamic style home loan or mortgage if the rate is attractive.
There might also be a yearly takaful fee as well of about 500 dirhams. Takaful is a group-type of insurance based on the value that if one member of the group requires assistance, the group can take of them. Another coincidence, this takaful payment is similar to western banks annual home insurance fee.