I would think the BHO extraction is not extracting everything, or is destroying something important (because of its toxicity). BHO is poisonous to life, so I like to avoid it.
As for the different effects from methods, I have read that the various cannabinoids interact with each other, so getting more compounds with CO2 can affect the way we experience the whole of it. For example, I read that CBD, CBDA, THC, and THCA all interact to give the patient a moderated experience, with all of the medical benefits. The combination of all of them change the perceived effects of all of them. If you want strong THC, don't use an extract with a lot of CBD or CBDA, as I have read that they temper the effects of the THC (reduce its psychoactive effect). I think it all boils down to what effects you are looking for, how the extract was produced (solvent used, stripping all or targeting some compounds, etc...), what compounds the strain contains, and what compounds are targeted for extraction.
I love this machine for just that reason. I can customize each batch for the particular needs of each patient -- giving them the components that will help them the most, excluding the components that cause the patient problems (THC for example), and by extracting the plant's own natural tempering compounds along with the active ones.
I haven't figured out how to do that with BHO or ethanol. I can customize each CO2 extraction.
As for terpenes, BHO/ethanol destroys them completely. With CO2, you can get them in very small (short extraction times), weaker amounts or very large (longer extraction times), powerful amounts, depending on length of time targeting terpene-extraction. Once you figure out how much Terpene is "enough" for you, you can get that amount by monitoring the time of extraction during the Terpene-phase. Most BHO extractions add an arbitrary amount of terpenes back, probably not even extracted from the same plant as the medicine. My CO2 process starts by extracting just the terpenes and if the extract is too flavorful, I can reduce Terpene extraction from, let's say, 45 minutes to 15 minutes and the result will be less flavor. (I've noticed that the dryness of the source material also affects the quantity of the terpenes. If it starts dry, there are less terpenes available, but if it's wet, I'll get a lot of terpenes, but then the cannabinoids don't come off as well [water interferes with the later CO2 extraction-phases, I am told]. This is my ongoing challenge, for now.)
Gosh, there really is a lot involved in doing this, huh? :)
Cheers,
COG