So I've been comparing the three sets of research rules- Original Research in HoH:TL and Hermetic Integration in Ancient Magic and Hedge Magic Revised Edition. The latter two are virtually identical (the only practical difference is the relative availability of sources of Insight, since practicing hedgies still exist), but the former is significantly different. The differences leading up to the breakthrough are generally understandable, but...
Passing on an Integration Breakthrough that results in a Hermetic Virtue requires a Mystery Initiation (likely to be beyond crippling, as there is no relevant Cult Lore, the Mystagogue probably has shite Presence, and the script will be experimental) or another Breakthrough.
Passing on an OR Breakthrough that results in a Hermetic Virtue requires a single season of personal instruction or a tractatus.
Original research is easier to pass on to other magi - by definition, the resulting breakthrough is entirely Hermetic, and easier to teach. But learning a Hermetic virtue through integrating hedge or ancient magic is much easier to accomplish the first time, because you have sources of insight and examples to study instead of inventing the entire thing yourself. Simply knowing that something is possible, without any other details, is a huge benefit for creation.
Think of it in terms of a (terrible) metaphor - integrating existing magic is similar to an English speaking student learning calculus from a Latin speaking instructor. Original research is an English speaking genius inventing calculus on their own, which is much harder. It's easier for the English genius to teach calculus to future English students, while the student who learned it in Latin still needs to translate it to English before they can pass it along.
Minor Breakthroughs are even easier to teach, only requiring a Lab Text for most of them.
There are some significant differences between Original Research and Integration. Original Research, while really pushing Hermetic Theory on the extreme outer end, is still a refinement and improvement of the Magic Theory that all Hermetic Magi know and use. Compare that to Integration in which you are trying to add something whose basis might be completely at odds with Hermetic Theory.
The results of Original Research are in your native language, while the results of Integration are in an unknown language you have to at least partially learn to be able to use. That second breakthrough on Integrations is what translates it from the unknown to native language.
That is not to say that Integration does not have its advantages. There are many things that can be researched through Integration easier than Original Research, if the Original Research is even possible. Just looking at the folk witches, the difficulty of their research for three effects that effectively break Hermetic Limits is two at 45 and one at 55. For Original Research they would be 60+ if even possible. Not to forget Subtle Opening for 30.
EDIT: Even at the same difficulty, it is most often easier to perform an Integration than an Original Research. The rolls tend to be easier and you do not have to spend time randomly inventing effects for possible inspiration to research towards the total.
I personally have the feeling that, while the systems themselves work slightly different, the Breakthroughs they provide are meant to work the same way. It's even possible to use Breakthrough points from both for the same Breakthrough (AM page 9, HM,RE page 16), in which case I don't really know how you could decide if it's an OR Breakthrough or an Integration one.
So I feel that the Breakthroughs from both systems are meant to be the same, using the same rules, and that any differences between how they are taught afterwards are either typos or inadvertent mistakes.
An OR Breakthrough is one done purely by OR. If you include anything else in it then you are inserting something not purely Hermetic theory into it.
The difference in their Breakthroughs is that ones made purely by OR are completely Hermetic Magic in nature. For ones that use any element of Integration then to make it as easily understood as a OR Breakthrough requires a second Breakthrough.
With the higher difficulty, slower pace, and Warping cost from OR you might actually be able to get both Breakthroughs through Integration easier.
part of this depends on whether you are bonisagus, and whether you want to publish. For example if my bonisagus magus wishes to start a cult to amass power she has to contend with the fact she s required to make her work available to anyone who asks. She is not however required to translate her lab notes. So she can make a breakthrough, not integrate it, set up an initiation for her cult, and carry on, while if she integrated it and wrote the tractatus of integration then anybody who asked would be able to get the virtue. That would gain her a lot of house acclaim, but dash her dreams of being a cult leader.
I think you have it backwards- integration requires a mystery initiation or additional breakthrough; original research a tractatus.
Edit: Oh. I see what you're saying. Integrate as in "make a part of standard hermetic theory for everyone", not integrate as per AM/HMRE for achieving the initial breakthrough (though you would in fact want to do that). In that case, yes, that's an excellent point.
That is an interesting argument and close to the one used in my Saga. We did enough to get good House Prestige (half of us are Bonisagus), then when we started building our Covenant Mystery Cult we didn't fully integrate our newer stuff. The leadership of House Bonisagus is starting to look like the big bad, so we want to help them as little as possible.