They're both being stupid but ultimately it's the management that are answerable to the shareholders.
In most airlines, the employees going on strike would lead to people in management being sacked. Prolonged industrial action is a failure of the management to manage their employees. It doesn't mean giving them what they want but it means reducing costs in a way which takes the employees on board. Most other airlines seem to be able to do it.
BA have an industrial dispute which will subtract millions from next years figures. Most people I know won't even book with BA if there is an alternative. It's time for WW to sort it out NOT prolong an industrial dispute by playing hard ball with an employees union over perks.