How to sell my skills in a research statement
What you write should depend in part on the type of job and the type of institution you are applying for. 

To apply for a research focused position in a high level research institution, your statement should reflect something about your suitability to work with them explicitly. So different statements for different institutions would be warranted in that case. Each with a different focus, but also showing how your other interests support your work in that primary field. 

For a more general position, say one that involves as much teaching as research, or the research requirements are more "casual", a general statement would probably be better as it shows flexibility that the institution might value. 

But in general, make it about how you fit the needs of the position.