It isn't possible to make a blanket statement here as both have their advantages and disadvantages. Here they are:
Disposable filters
Easier to clean because the coffee grounds can be disposed of together with the filter
Different versions as they are adapted to the variety of coffee
New filters have to be bought regularly (higher costs, damage to the environment)
Permanent filters:
Experts claim that a good quality permanent filter results in a superior flavour of the coffee
It isn't necessary to buy new filters all the time (cost saving, environmental protection)
More frequent cleaning requirement, leading to higher water consumption
Can’t be matched with the type of coffee