It is speculated that .edu and .gov still hold alot more weight then other domains. However some might argue that backlinks using keywords to your site would be more effective especially when linking from high ranking relevant websites.
.edu and .gov are regarded highly; but remember that the highest impact inbound links will be the ones that tie your content together. So if you have a website about being a mechanic, you don't want to build inbound links on websites about dogs. This is because when crawlers start linking all the websites together they are going to go from the site about dogs to your website about being a mechanic and realize that the content has nothing in common. Which if you are using online directories to get inbound links you should be focusing on putting the links in the appropriate directory not an unrelated one.
Now as of for inbound link keywords. If you are writing a guest blog post, having links that might say "Bay Area Mechanic Shop" is going to be alot better then a link that says "My Website". As some crawlers take into account the inbound link text. It isn't a massively huge deal but it does help.
Acquiring even a few high backlinks from .edu or .gov sites is very effective than other backlinks.However it is difficult to obtain backlinks from these domains.Anyway , you try to get these backlinks.
Certainly .edu and .gov has more weight on back link method. But I prefer submit your site in relevent websites so that avoid future penaltly from google. Google will prefer backlinks from relevent sites.
I used to make many EDU links to my site but majority of them disappeared this year, which made my ranking dropped.. I will have to keep searching for this EDU links as we both know EDU links is usful than other normal ones..