The best links are those which are relevant. Relevance
outweighs authority. Google does not treat .edu or .gov differently to other domain extensions. It's quite possible to have a .com and a .gov linking to you and the .com being a better link. What's important is understanding the context of the link. How are you being linked to, where (profile link Vs contextual link in a main resource page), number of obl, PageRank of the page, relevance of the page etc.
If you can get a link (even no-follow) from a relevant and high
PageRank page with low OBL then great. Let's say it's a resource page on student personal finance and you get a link to your page on personal finance tips for students, there's a small number of obl. That's going to be a great backlink to have.
If your wanting a link just because it's .edu or.gov I don't think it's worth your time. If the link is easy to make then it's probably going to have very low PageRank and not have that much value for your website.
For example getting a profile link is not going to be very beneficial as the page will be so many clicks from the homepage that there's not going to be much PageRank on it, which means you'll get little to your website. Secondly the value of the link is further diminished because there's little relevance to your website's topic as your link won't be surrounded by lots of content that Google can understand the reasoning and relevance behind the link.
The same goes for scholarship pages. They might have better PageRank because they'll likely have more internal/external links pointing to them but again there's little relevance to your website and the OBL count will be very high, thus reducing the value of the link juice.
Don't get a .gov link for the sake of getting a .gov link. The value of the link is determined by loads of factors and not the fact it is a .gov.