Here's me break-down of the three (all three of them are excellent, but have notable differences):
Albion Meyer: My favorite for drills and free-fencing, since it's the liveliest in feel. It's probably the best of the three for full-speed bouting, since it has a relatively light blade-presence with nice thick edges, and decent flex down near the "sweet spot" to absorb thrusts.
Albion Liechtenauer: This one is best suited to stage-combat and controlled drills, IMHO. It has a very realistic weight and balance, and the blade profile is designed to look and feel fairly real as well. That means it'll perform more like a sharp sword in the bind, and look good to an audience. The problem is that it has thin edges, so it can really hurt to get hit with.
A&A Fechterspiel: A little more blade presence, and slightly less flex, when compared to the Albion Meyer. Nice thick edges, but since it has a little less give, it can hit slightly harder. This is a mixed bag compare to the Meyer, since it's just fine to use in the same contexts, for the most part, but the extra stiffness makes it really good for practicing harnessfechten and doing half-swording. The Meyer is just flexible enough to make some of the half-swording stuff a little harder to do, and the Fechterspiel has just enough stiffness to work really well with it.