I'm a graduate student who is finishing off this Summer. I currently have two postdoc offers that I am considering, and they are very different in nature.
(i) Postdoc at a prestigious university, without belonging to a lab/PI, and is essentially a "do whatever you want" postdoctoral fellowship. I can choose to get involved with a specific group or not. (ii) Government lab that is affiliated with a well-known university. I would be expected to spend 50% of my time on a project they assign me, and the other 50% could be spent on whatever I want to do.
They are both very well known places in and out of academia so I don't think there will be any advantages/disadvantages of picking one if I decide to quit academia and go into industry.
I can see that I will have a lot of freedom for (i) and I will be surrounded by brilliant postdocs so it will certainly be a stimulating experience. However, I can also see the possibility of getting absolutely lost without the supervision of a senior faculty member. The institution also happens to have no faculty members who are directly knowledgeable in what I am working on. However, said in another way, it would be a very good opportunity to learn about other projects.
On the other hand, for (ii), I will have a safety net because I will belong to a particular research group, and there will be other members to support me in finishing off the assigned project if I get lost (only if I ask for help, and I don't they will be pushing me around). There is, however, a chance that I will be spending 100% on the assigned project (because that is where the fund comes from and it is the priority) with 0 freedom. In contrast to (i), it is very likely that I will be interacting with a narrower spectrum of people in terms of science so it will be harder to broaden my horizons.
Does anyone have any experience with these kinds of postdoc jobs? How important is it to have someone senior down the corridor who is an expert in what you work on? Did you have a problem getting recommendation letters for a postdoc position like (i)? And finally what was your overall experience?
(I don't have enough reputations to comment so I will add here)
Edit 1: (Thank you for your input AJK!) I belong to a large collaboration and I do have opportunities to interact with notable professors regularly, but only through emails/chats. Since this is the way I have been working already, I think I will be fine (in terms of getting science done), but won't be gaining much compared to my current situation. However, I have a feeling that recommendation letters will shape very differently. If I go to (i), my recommendation letters will be coming from professors who I interact through emails and telecons. Whereas if I go to (ii), it will be from the project manager who I will be interacting with face-to-face on an almost daily basis. Of course, the content of the letter will heavily depend on the quality of my work but is this not better?
I should also clarify what I mean by "directly knowledgeable in what I am working on". There are people in the department working on the same topic, but those professors are more focused on building the instruments, whereas I am more theory/data analysis person. Granted, they are very knowledgeable and they probably know a lot about data analysis too, but I'm not sure how keen they are in discussing technical details. So yes, "if you are just saying that you work in general in a field X, and a subfield Y, and want to use technique Z, but there are no Z experts" <- this is what I meant.