Quarter wave back loaded horns have a constantly expanding cross section to the folded horn. That expansion prevents standing waves from developing in the horn. A transmission line has a more constant cross section and has to have a lot of damping material in it to reduce standing waves. This damping greatly reduces the amount of acoustic energy that back wave can contribute to the sound, hence the much lower efficiency of transmission lines. But, it is a much harder trick to make that back horn have the properly expanding size and the opening has to be quite large.
Differences Between Folded Horn Speakers and Transmission Line Speakers
I've been looking at various DIY speaker builds and came across a folder horn speaker and I've also seen transmission line speakers. I've tried to google the differences in the two, as they look similar, but I suspect that there are differences. The only visual difference that I've noticed (I've only seen one folded horn, so the comparison pool is very small) is that the folded horn seem to have a larger opening than the transmission line speakers. Maybe it's just the one speaker that I saw, so I don't know that would always be the case. I'm hoping someone on the forum is much more knowledgeable about these things than I am.