The tolerances in 3D printed fitted parts can be annoying. It might be nice if we could have a null space defined in the designs so you could properly control them. That way, things like shell thickness would not make parts fit poorly. Things like printer wobble would still be an issue though.
Cura and Slic3r are what I use. I print mainly stuff designed by others.
Designs should probably be made with tolerances in mind too. The are some areas where it is a good idea to increase the tolerances like corners.
@NathanielStenzel it is really tricky, the gap required on yours is probably very different then mine. If I make the gap too big it will not stay closed on my printed, but may just barely fit on yours. My printer lines a .1mm gap to make boxes that close.