What you are talking about are two different problems, that probably require two seperate solutions.
HITH is usually associated with the presence of Hexamita and/or Spironuclus bacteria. The bacteria are usually kept under control using a proper antibiotic.
HLLE however, is now thought to be an auto-immune condition precipitated by enviroment or social stressors.
Evidently numerous attempts at isolating a guilty pathogen have failed, making the choice of which chemical to use completely unwarranted.
I personally only keep South American cichlids - those who keep Rift Lake Cichlids do not often meet with either of the above problems.
However with SA fish we do seem to get this problem.
Yes - it is brought upon by a lack of plentifull water changes, but it is also thought that this may be coupled to the feeding of too large a food items to some SA fish.
In particular I keep satanoperca and Crenicichla - I havnt had either in Crenicichla but I have had it a couple of times in some Satanoperca -
I would say that it seems to take hold in only certain fish - ie I have had it in S.acuticeps and S.daemon - but not in S,lilith - I have also had it in S.leucosticta but not in either S.pappaterra or S.jurupari.
The judging is still out on this one, we probably need a good fish based scientist to take hold of it coupled by a few dozen expeirenced SA fish keepers to have a go at coming to some sort of conclusion on both the subjects.
I have heard people try to say that the two are the same - but they are not -
The answer is out there - Ive done an article for the BCA on the subject - we shall see