I personally trust .edu domain much more than .gov domains. But that's probably because I am a bit biased coming from a academically minded family background. With an exception of my father.

It depends on the web site itself.

.gov because the government owns those.

Uh oh, not an either/or answer for me. I love research. I use both of those domains, Stats, historical documents, records from different branches of the government all at .gov sites - plus all the records I've researched for family history re: military and pension service, immigration, census records, more. Yes, may run into more "slanted" materials at .edu sites - but know that going in - and am likely to find many more "topics" - and certainly many more interpretations, opinions, collections, etc. Like that I can find both original research "and" interpretations - but usually clear which is which. We know different domain types have some measure of "bias", funding, content types we expect to see (or not), sources and owners of sites, etc. So trust is ok for me on that basis. Have more trouble with one dot com site vs another - where sometimes it's masked or unclear who owns it, what their "agenda" is, etc. That certainly affects my trust levels of content found there and how I "weigh it" vs .gov or .edu sites. So? I'll take both and go both deep and wide into any topic I like. Add a bit of dot com just to shake things up. Keep part trust / part skepticism. Lay that all out - shake it up good - and decide what I make of it all. Life is good! :)

Between the two, if I needed information about a government program I would trust .gov For most other uses, the .edu would probably be my choice.