Greetings,
Not having played a lot of games I want to know, in your experiences is there a decided benefit to spending points in Teaching vs. Scribing?
Obviously each has its own benefits. But in a game, setting up a covenant, and playing the characters out for, say, 20 seasons, is there a marked difference in the overall benefit to the covenant of one Ability over the other?
Thank you for your time.
If you are only playing 20 seasons, Its probably not worthwhile to buy either one.
But... in general it is better to write books than teach. Written books, especially tractatus, can be used by multiple people over time without taking up any additional time from the author.
Teaching an Art grants a pretty good chunk of xp (Com + Teaching + 9 vs Com+6 + bonuses for Tractatus). But not as much more xp as each studying independently would provide. Teaching vs tractatus writing only pays off if the covenant is really small, such that trading off teaching is better than trading tractatus.
Of course, teaching is like a Summa of the character's full Art score and you can't run out the ability to teach.
ehhh, just realized I kind of didn't answer the question..
Scribe's value is hard to calculate. If you can reasonably trade for the right to copy books on a regular basis, its better to copy those books. However, Scribe only really matters for Summae and most of what you will be copying will probably be Tractatus.
So.. while writing is better than teaching... Scribe's value to writing is pretty minor. So you may want to take Teaching, but spend your time writing and copying anyway 
And for copying lab texts.
Teaching is good for spells, but you need neither skill for it.
Otherwise, writing Art/Skill books only is worthwile if you have a Com of 3 or more.
For arts and skills: reading a Primer (Q21) beats teaching. Primers are widely available (see Semita's library, covenants)
Scribing is helpful at level 1 + specialty "orderly". Otherwise, I recommend making some magic item for the covenant (any item) and use the money saved to employ a scribe.
Care to explain why you think that is true?
Well, if you want to min-max, I recommend to start with a teaching score of 1 (This way avoiding the -3 penalty if you need to teach at some point...) and a scribe score of 1. (If at some point only a mage is allowed to copy a text. Again to avoid a -3 penalty)
For day to day work of copying I would purchase a specialist at convent generation, or acquire one during a story later on. This way you do not have to spend a whole lot of XP on an ability you rarely use. But what is even more important: This way there is no magus who has to do all the copying work and thus cannot take part in adventures (or leave his project). On the other side, this would make for a good character of the alpha-SG as his character will most likely be consumed by library work and therefore has a good reason not to leave his home...
In short terms: Invest a few XP in either ability, which makes sense as all apprentices will have to do some copying during their apprenticeship, and all pupils do pick up some ideas about teaching, when being taught over 15 years.
We play a slightly longer campagin So far about 150-180 seasons or 45ish years.
We have found that books are no-where near as good as teaching. Teaching will provide a base of 3 + Teaching + 0/3/6 for number of sydents + communication.
I play 2 characters, A Magister in Artibus companion and my Flambau Magus
Artibus
Com + 2 Teaching (Groups) 5 +3 + 1/4/6 for group number (modifed by speciality)
for 11/14/16 points in a single season.
Add strong teacher (which he has) to that and it raises to 16/19/21
Flambeau
Com - 2 Teaching (one on one) 4 + 3 + 0/3/7 (Group modified by speciality)
for 5/8/12 Points in a single season.
I've always felt teaching the bette rotpion with 2 points.
It takes out to seasons to teach (the Teacher and the learner)
Would one magi let another into his lab to teach him for a whole season, or spend a whole season in anothers lab.
Two of our Magi are close friends (despite the fact they utterly hate each other) and because they have been covenmates for 40 years ar enow close enough to OCAISSIONALLY do that.
If you have a covenant of four to six magi, the book will beat the teaching, at least for Arts. The teacher gets Exposure (2xp) and the Student gets say 12xp (Com 0, Teaching 3). The tractatus is worth say 7xp (Com 0, +1 Resonant materials). If its just the teacher and student, obviously the teacher is better. But if you have five potential readers, the balance changes. Now five people each get 7xp and the teacher gets his 1 season of exposure and 4 seasons of real work compared to having to teach five seasons. The /teacher/ clearly wins by writing the book. Aggregate xp might be slightly less, depending on what the teacher does with his 4 free seasons.
Additionally, the book exists to be traded for other books or be used by guests, apprentices, etc. The lecture series is one and done.
Further, the tractatus is useful to any magus even if his skill is equal to or better than the teacher's in that Art.
Oh, btw, I don't see any reason why the teaching would need to be in one or the other magus' sanctum. Teach in the library or the garden or whereever.
Teaching shines when you can teach a large group, especially a group that is not literate.
It depends what you're teaching. I think it fits thematically that magical arts or skills would require a lab to explain and disect even if they don't distinctly count as lab work. Afterall in covenants there is a 'teaching' modifier that can be applied to Labs.
The only issue I'd have with your comment about the book is How long does it take for the teacher to prepare the book. Because Summa's take longer. Tractatii take 1 season.
Well, I didn't particularly discuss Summae. That's a far more difficult topic because the value of the book is limited by level, but the quality can be hugely better than teaching if the student is able to benefit from the summa.