In my mind, it depends on the size of the acquisition. For very small acquisitions one team may play different roles provided they have the skills and expertise to do different types of work at different times during this process. Generally, however, it would seem to me that there should be 2 separate teams working in tandem from as early in the process as possible would be the best bet. This is because of the skill set difference and the need to have dedicated team members.
In one of my previous company, we had separate M&A team and Project Management teams assisting with the process.
The role of the Line management is also very important to one hand keep the lights on by ensuring that the BAU activities are being carried out per plan but also modified processes are also being incorporated. I would also depend on them to do the bulk of the Change Management with their team members.