Should I use OwinContext's Environment to hold application specific data per request

OWIN environment dictionary can be used to store per-request data. Properties collection of the request object can be used to do the same.

The main difference is OWIN environment dictionary is an OWIN concept and is applicable to any middleware running in a OWIN host. Properties collection of the request object is an ASP.NET Web API concept and is applicable only to that specific framework.

BTW, ASP.NET Web API itself runs as a middleware in OWIN pipeline. So, to answer your question, you cannot access the request properties collection of Web API from your middleware because it is applicable only to Web API middleware (or that specific framework).

If you want to write your cross-cutting concern stuff as OWIN middleware you have to use OWIN environment dictionary. If Web API extension points like a filter or a message handler is okay, then you can use the properties collection.

Obviously, anything you write leveraging Web API extension points is applicable only to Web API whereas OWIN middleware is applicable to any kind of app running in OWIN pipeline and that includes Web API.