The question is too simplistic, soft skills encompasses a wide range of skills and anyone responsible for delivery will need a mix of hard and soft skills to get the job done. However, in the case of project management, it is the 'management' element that is the key to which soft skills are needed. Management requires an understanding of how to communicate and work with stakeholders and motivate team members.
In contrast, the soft skills of leadership are needed in environments that have been less defined. Often situations that are necessary to be dealt with as they are required to get the project delivered but are not to do with management.
Sometimes project managers are expected to be leaders. Both require soft skills, I would argue different ones. This makes the debate even more complex.