We got three quotes as we are moving to Australia in a couple months time.
We got 2 Swiss companies - Keller and Swiss Moving company
www.thesmc.com based in Lausaune and then an Australia moving company. The quotes from the Swiss companies were about the same and said that we only need a 20 foot container. However the Australia company's price was almost double as they said I needed a 40 foot moving company.
In each case the international mover would contact a local mover to view your house and personal effects to determine how much cubic space is taken up. This occured for both the Swiss Moving Company and the Australian company. However, the keller company have an office in Basel so they did not need to contact one of their network movers.
Other thing to be mindful of is what time of service is required full packing and unpacking or where you do some of the packing i.e. non-breakables.
Insurance also varied depending on the company. It ranged from 2% to 4.5%.
I hope this helps