Postdoc vs Assistant Prof - which is better for a career academic? All questions are hypothetical as of now.

I work in the health / biomedical sciences. I have been a postdoc for about 2.5 years and had to leave the postdoc after the lab closed. I have been interviewing for both junior faculty and postdoc positions for the last 3 months but none have worked out (pay cut, rejection etc)

I have an upcoming postdoc fellowship interview with X lab in University A, which I applied for towards the end of the application deadline 1st week Feb. The independent academic committee has determined I am fully qualified for the position and no rebuttals were needed (unusual I know; this is a Scandinavian university). This is a position that will take me out of my comfort zone and give the opportunity to develop new quantitative skills - if the mentors are good (YKWIM). This project is supervised by 2 mentors and both have very impressive h-indices, and one very experienced researcher and another younger researcher but very impressive credentials. I will have teaching responsibilities.

However I applied for an asst prof position in Y lab/dept in the same uni A, which has a much later application deadline. I believe I have a good chance of getting this gig because I have run many projects in this exact area of research and have all the training and certifications needed. I guess I won't be developing any more technical skills and moving on to project management / teaching / administration. This is unique as the position already comes with a project and a longer term of employment, and is still supervised by 1 prof. The yearly salary is not much different from the postdoc and the potential impact of the research is lower.

The academic's goal is to get a faculty position but it seems the asst prof position would be of little value since this is not my grant. It is also not clear if this is a tenure track position.

Hoping I could get some advice from more experienced researchers because my focus  is on building a career, although I do hope to make great scientific achievements in the process.

Cheers and I'll be hanging around if anyone has questions.
In the US, I think it would be clear that the assistant professorship is preferable to a post doc in nearly every case. The exception would be the opportunity to work with a superstar as a post doc. 

Again, in the US, assistant professorships are (almost) invariably tenure track, though there are a very few colleges that don't offer tenure at all. But that isn't likely to be a factor. 

For most, a post doc is really just considered to be a stepping stone to a real position and a way to continue to advance if the job market is poor at the time. 

But ask the institution itself about tenure and also about the likelihood of actually earning it.