It's not a case of which is most used; the terminology is different in British and US English. 'Mobile phone' is used in British English and 'cell phone' in US English. In the UK it is the same as in Australia, we say 'mobile phone number' or more commonly just 'mobile number.'
Presumably they use 'cell phone number' in North America, because they have a different name for them.
People don't really use 'landline' that much. We say 'house phone number' or probably more commonly 'home phone number' instead.