I know from myself and from my friends as an engineering PhD student in the US, PhD students are vastly divided into two:
- The ones who expect every step, every single instruction and idea from the advisor. They are not much of a help if you're looking for self starters who fly their own tangents. These are mostly clueless students who do not know why they do PhD. They are good at programming, modeling etc. as long as they are given whatever the job is or idea is.
- The ones who push for new ideas, new methods, and does not only work on what you suggest for project progress but also conducts what s/he thinks would work better. They have tons of ideas to conduct, they enjoy what they do. And mostly, they like to learn as much as possible, so they are more flexible rather than focusing on one single thing, which is whatever the dissertation is about.
From 2 PostDocs I have worked with, in my lab, I have observed:
- They are more focused in one area, and mostly wanna publish/research in that area since they like to pursue academic career afterwards. The research area is mostly related to their dissertation or kind of continuation of their dissertations "future steps", so they are not always as flexible as a PhD student.
- However, they have better discipline,and better time management and organization skills. They can easily kick in a project.
- Mostly, because of their experience, they are more able to or better at looking at big picture rather than getting lost in details, compared to new PhD students; which is pretty necessary to be on time with projects timelines because postdocs are generally much faster and more efficient.
Of course, my observations as just a PhD student may not necessarily be useful for you. But if I were in your shoes or when I hopefully one day get to a similar position, I guess I would devote 1 quota for each if it is possible. 1 for a postdoc who has proven to be"all-over-the-place" but also expertise in one topic, so depth-and-breadth together; and also for management and organization skills. And the other quota to a PhD student to be flexible in research to do. But while choosing PhD student, it is necessary to be able to differentiate whether the student is a self-starter and self-willed or "requires-to-be-managed-at-all-times."