The main design that we've mostly used for the last 20 years is the double miter Direct Internal. This design holds up beautifully for heavy duty touring, racing, or just about any use. It gives a responsive ride, and can be built with very light tubing if we ovalize the tubes. We believe it is the best frame design to use when high performance is required either for heavy duty touring or light weight racing.
Lots of manufacturers make the direct internal design, but most use a single miter method. If you would like to read a detailed article on the differences between double and single miter method, read this.
The ST design is used for building tandems that do not require the lateral rigidity that we can get with the other designs. A lot of people wonder if this design is lighter because there are fewer tubes used. No, this design is actually a bit heavier as we use heavier tubes to ensure strength. The advantage to this design is that it is less expensive because it can be built with less labor. It's basically a Marathon design (see below) without a top tube.
Here's a design that we still use when the captain is a bit shorter legged, and weight is a concern. This design, and variations of it, were quite common in the 1970's and 1980's, but current day it's not a dominant design.
The Marathon design is an older design that we built many times, although not as much in the last 20 years. We found that the use of modern materials means the frame doesn't really need to have this much tubing to be strong. The direct internal design does a better job of isolating the rear bottom bracket, so this design kind of went the way of the Ford Edsel in our shop. We're happy to build a frame with the design for a custom who prefers the look.