Post-doctoral research statement/project: current/future vs thematic
I would favour option 1. 

You are trying to tell the story of your research career so far, and how your story could continue at the institution(s) to which you are applying. Looking at it in this way, you are casting your past and present research activities as "Background". 

Your subsequent sections would be about specific projects - the "Future". In each section you can refer to your skill set, showing how this project is based on a firm foundation of skills developed during your Background years.

A reader will get a much clearer picture of you as a scientist - past and future - if you structure your application this way. It makes for easier reading, and you want your admissions committee to be happy. 

Splitting up your "story" thematically - showing how parts of your background set you up for the project under consideration - makes it more difficult for a reader.