There have been quite a few topics on compasses but not much has been said about the different types. Here's my take on them:-
The baseplate compass is a "standard" for walkers and other land navigators, when used in conjnction with a good map. Its good points are:
1) It's very light and makes a very good portable geometry set for map work, assuming that there aren't significant alignment errors in manufacture (paying a high pricce is no guarantee of this, I've found).
2) It's "set and forget". Apart from allowing for Grid Magnetic Angle (GMA, often erroneously referred to as "declination" - see my other post(s) about that), you just set the bezel on the map and follow the heading obtained. You don't ever even have to know the actual bearing, unless sharing it with others. Some compasses even allow you to preset the GMA so that you don't ever have to bother with actual numbers of degrees (or mils) while on the move.
3) It's a tolerably good marching compass - easy to use and quite good enough to keep a course to about 5 degrees, which is realistic.
The baseplate compass is really poor, though, if you want a reasonably accurate EP or fix (I'm thinking backbearings and sighting maybe distant landmarks). Specifically, you can't sight the target (at eye level) and set the bezel at the same time. You have to move the compass, without rotating it, to do each thing, or you have to blue-tack the aligned compass to a stable level surface (if you can find or make one above ground level) and move your viewpoint.
The mirror compass solves the major part of the sighting problem by allowing you to see the target and the compass arrow at the same time. However, they are in different focal planes and it's still difficult to manipulate the bezel while trying to maintain a steady sighting.
The types of compass above fulfil most walkers' needs most of the time but if you care about having the right tool for the job, then the baseplate compass and its "mirror" version don't really cut it when it comes to sighting objects. The prismatic compass is the longstanding favourite sighting compass for perfectionists. Unfortunately, this type of compass has fallen out of favour for use specifically on land. Decent models are either antiques (very expensive) or high-grade surveyors' instruments (even more expensive). Fortunately, they are still widely available for marine use and work just as well on land! I recently bought a Plastimo one for about £50. OK, even that price is a bit self-indulgent! Unlike normal walkers' compasses, a prismatic compass does not have a bezel. Instead, the compass needle carries with it the entire circular, calibrated compass "card". The compass bearing is read directly and there is no setting to do by hand. Thus, such a compass can be described as "read and remember", rather than "set and forget". The really important thing about a prismatic compass is that it allows you to view the target and the bearing together, with both simultaneously in focus.
The ultimate prismatic compass comes combined with binoculars but, for most of us, that's overkill on weight and/or cost grounds.