Which country is going to be their main destination? That's the governing factor for the application. From swisspea's link:
"He or she must first identify which Schengen country is the main destination
. This determines the State responsible for deciding on the Schengen visa application and therefore the embassy
, high commission
or the consulate
where the traveller will have to lodge the application. If the main destination cannot be determined, the traveller should file the visa application at the embassy, high commission or consulate of the Schengen country of first entry."
If they're going to be in Switzerland most of the time they'd apply to a Swiss embassy/consulate. If it's another Schengen country then that's where they should apply. If they don't know then it should be the country they plan to enter first.