I know that both LSCM and ABH both measure the angles on the mesh but I was under the impression that quads rather than tris yielded better results.

I've seen no evidence that points to triangles giving a better UV result. I do know that quads are typically far easier to unwrap, because you can select edge loops, and create seams much faster. Edge loops usually cannot be selected easily or reliably on triangle faces, as you know. I'm not sure it matters as far as what algorithm is being used. The algorithm of the unwrap does not depend on how the faces are divided as much as it does how and where the seams are created.

Also, don't forget that at the moment things are getting unwrapped, either with Least Squares Conformal Mapping (LSCM), or with Angle Based Flattening (ABF), the internal algorithm is breaking down the quads to tris anyway internally. This is the same with render engines. So using quads is merely easier for the user, but the computer sees everything as triangles.

Not sure if you've used it before, Mark, but 3D-Coat has come up with a new unwrapping algorithm that is superior in most cases to the LSCM or ABF algorithms. Global Uniform Unfolding (GU) was introduced in 3d-Coat 4.1, and tends to produce even less UV distortion than the other two.

3D Coat Gets New, Improved UV Algorithm

I've used this on my most recent models, and find it very useful. In fact, I've decided to move my entire unwrapping and texturing process, for every model going forward, over to 3D-Coat because of this.

Thanks Lux, that was informative to the max.