Ake: Excellent question and part of the difference is that ASL is running a pentode tube in triode mode. I am not very technical myself (though have been doing a little reading in order that I can refurbish my own tube gear) and my understanding is that the SE amps using pentode tubes (in triode mode) are not directly heating the output tubes. SET amps using "true" triode tubes are generally directly heated (which many feel creates a different type of sound).
Perhaps there should be another widely acknowledged designation for these amps (I know that Audion, in the UK, uses a different one for their models that use pentodes in triode mode)? Some tube amps seem to switch over to another mode @ a given output level (like certain SS amps) and these I do not understand @ all. I went to the Decware site and, yes, they use the term SET (though the amps are based on pentode tubes). I did not look @ ASL's site as I could not locate it.
I have only listened (seriously) to two amps that run Pentodes in SE triode mode (one being an early version of the Zen and the other is a small vintage SE EL84 amp that I currently own. Both of these sound different than push/pull to me, but without the added/flesh reality that I have heard from 2A3 and 300B SET amps. This could be due to the expense/build though as the true SET amps cost 2 to 6 times as much as the Zen, which retailed for $550 back then.
To make things even more confusing, I can easily modify the EL84 push/pull amp (which we are using in the living room) to push pull "triode" mode (it's currently running in push/pull pentode). Doing so will drop the power by half, or so, and alter its sound. I think that some of the ASL amps already come with such switching capability (pentode to triode), which might be nice to have.
I have forgotten the ASL designer's name, but he frequently answers questions in the audioasylum.com tube forums (they have separate "tube" & "SET" forums). You may find other owner's of the ASL models that interest you there as well. Also if you go to the FAQ section (@ the top of the main page) you will find the tube link that I listed as well as some nice "guidelines" for matching speakers to flea/fly watt amps (to be taken with a grain of salt as also noted in the article itself).
This still takes us back to the fact that you really need to hear the specific amps to understand their sound. The sound of these types of amps can be much more diversified than that of most SS electronics and if you are like me you will love some and hate others.