Sometimes, when downloading software from the Internet, I find that there is a .deb package ready for either my Debian/Ubuntu and also a tarball to be compiled. In the beginning I would simply use the package for its ease of installation, and wouldn't even dare attempting to compile. Even the sound of it scared me a bit. Nowadays, however, when I have the option I sometimes find myself in a dilemma: is there an unpopular advantage to compiling from source compared with the .deb package? I hope to find out here, thank you.
If you don't trust whoever built the deb or want to modify it, then you want to build from source. Some modifications are implicit, such as linking to different libraries you have, so building from source might fix problems if the deb was built against different libraries than you have.