Move from my current university or stay with a longer term proposal? I'm currently in a disjunctive regarding my professional life, and I would like a bit of an advice.

I'm finishing my PhD next March (is Japan, so is 99.9999% sure that I will finish), and I have 2 proposals.

One is to move away to US, with a very demanding professor in an experimental environment (I do mostly simulations), he seems well connected there with people in good Universities (MIT, Stanford, UPenn, etc). Yet, he himself is not very well known in my particular field, he is in his own application field though. The University is in California with what I guess is a standard PostDoc salary for a one year Post Doc program.

The other is to stay in my current University, with my professor in a more stable and long term proposal (4 years). The problem, is that my professor was never very engaged in my project, and I got mostly marginal help from him. He was always really helpful, and had good resources (conferences, equipment, etc).

I would like to know the opinion of more experienced people. I would really like a future in academia, so I'm open to any suggestion.
Noöne but you can make this decision, so here are a few thoughts that sprang in my mind when reading your description. I hope they can be of help in your decision-making.

It looks like your option #1 is more of a gamble (which might be a pro or a con depending on your own character!). It seems that you would go to this new group and change your research topic: if so, you have to realize that a one-year position is quite short for learning/adapting to a different area of research. I think it's good for a post-doc to actually pursue something different than he did during his PhD, but it is more risky on a one-year contract.

Second thing: if you go option #1, would you be burning bridges with your current place? Or would they welcome you back after your one year of US experience, if you don't find another post-doc in this new (sub)field? If you think you can pretty much fall back to option #2 in one or two year's time, then option #1 sounds a lot less risky.

Finally, being a rather “independent” post-doc (i.e. working with a professor who's not fully involved) has some advantages if you can handle it and find intellectual support in other ways (collaborations, conferences, visiting positions, …). It allows you to establish yourself as an independent researcher, which is a first step to become a group leader yourself.