The answer is a mix of both.
For any project, a Project plan is a must as this defines your mile stones.
The mile stones are major achievements in the project that are to be highlighted.
These milestones are then broken into smaller quantifiable "bits" and man days are put against each "bit" of work.
People are assigned against these "bits".
Pleople have different skill levels, and as a person responsible for the success of the project, you have to have each task time bound.
So if you do not have time frames and task assignment, projects shall slip... as people have different level of aptitudes for tasks..Some people can do some tasks better than others, so if you assign tasks to people, you shall get a better result, rather than having a LIFO sort of an arrangement, as then you would not know who is being assigned a task. Tracking is also difficult in such projects.
PM
As using option 2,