I'm Currently waiting on a @progodlegend to get off a phone call and have found myself answering some very similar questions or seeing the same question asked over and over again about the upcoming patch.  So your getting a general super summary post about the upcoming mechanics and stats as i currently understand them.  There is another thread that has most of this in it but its spread out over many pages and shows the entire evolution of the sisi deployments.  If you spot errors shout them out in comments and ill fix in OP.

Refineries are a new structure coming in the new lifeblood patch on October the 24th.   They share the same mechanics as there Citadel and Engineering Complex Brethren, but are focused around the replacement of POS moon mining and reacting of the moon materials used in the production of t2 modules and ships.  This is a big huge change hence why there has been such a large reaction at the alliance level.

Quick Stats Stuff, and small but notable changes -

Tatara BPO Current Seed price on sisi: 40 bil isk

Athanor BPO Current Seed price on sisi: 5.5 bil isk

New anchoring mechanics.  Anchor, 15 min vuln timer, 24 hour invul timer, 15 min rep timer - Structure online.

Moon mining is switching from passive (set and forget) to active AKA must be mined with hulks, rorqs, t1 exhumers and the like.

This is a pretty massive change, since introduction all moon mining in eve online has been a passive activity managed by a relatively few number of people.  This has kept prices fairly consistent and predictable.  You set up your extraction then basically just shipped to market.  Supply was a very set in stone statistic.  This change to active mining throws everything up in the air how it will effect the price of t2 ships and modules is very much unknown, anyone who says they know the answer is fucking retarded and is lieing to you.  General guess says prices go up but no one can say with any certainty.

General Mechanics:

You set up your refinery on a moon, you then fit a module called a standup moon drill, provide fuel and turn it on.  This then allows you to set an extraction schedule that ranges anywhere from 7 days to 58? (I believe) days.  This is a linear effect the amount extracted per hour is consistent no matter what length the cycle.  This does allow you to however determine how much mining you or your corp want to do on explosion day.  Do you want to have a short mining day on a very regular basis or a play eve for 8 hours day once every 2 months.  This change allowed a lot of customization of your PVE gameplay.  After the set extraction time the moon asteroid pulls up to the refinery and you have a set amount of time where you can detonate your moon chunk into a belt.  This allows you to control the detonation for the time (within a limit) that is best for you and your corpmates to mine the material exploded.   The asteroids decay, so you want to be ready once the belt detonates to scoop up all that ore.

Speaking of ore it now includes minerals as well as moon goo and must be refined.  There is a whole new set of skills the effects the reprocessing level of this moon goo.   Each ore has a different composition much like you would find in a regular asteroid belt, it just includes moon goo in it.

After moon ore is mined and reprocessed we get the new reaction system.  This also has its own set of new skills that are modeled almost exactly off of the industry system currently in the game.  Use blueprint, set run count provide moon goo and fuel block input, x time later job completes and spits out processed or advanced moon goo.  This allows for individuals to engage in reactions in a way that was previously barred by the corp roles system.  It however puts the onus of moon output and production under the much more fickle and unpredictable market of the general eve membership for better or worse.

This more or less sums up the general mechanics of the system, corrections are welcomed.

Theory:

The choice between medium and large refinery:

The big difference between medium and large refineries is one part cost, one part bonuses, and one part fitting.  Athanor cost roughly a bil, tatara the large costs roughly 8-9 bil.  The big price difference is in the cost of rigging them.  700 mil for t1 medium, 3 bil t2 medium, 7 bil t1 large, 20-90 bil t2 large depending on rig.  The medium refinery has a 2% bonus to refining (on top of rigs) and 20% reduction to fuel consumption of refinery/reactions service modules.  The large has a 4% refining bonus, a 25% bonus to fuel consumption and a 25% bonus to reaction job length (reduction).

This suggests that in general the large is most useful for centralized reactions, and refining for all ore types.   This however raises the barrier to a perfect refine rig wise by 70 ish billion isk a formidable new sunk cost that adds a lot of additional choices when setting up an industrial operation.

There is one additional consideration however, the large has a damage output similar to that of a fortizar where the medium is a bit weaker than an astrahause.  On the right moon a Tatara could be considered worth it for allowing mining operations in systems more prone to hostilities or campers.  (belts spawn in weapons range of the refineries).  Having the anti-capital umbrella of a tataras launchers could significantly deter or raise the barrier to entry of an enemies hot drop.  Ultimately that choice lies with the user.

Rigs:

While there are rigs that bonus reaction output, im going to focus on rigs explicitly related to extraction.

Stability Rig: Increases the the time window where you can detonate the belt, very useful to control when to start your mining operations

Efficiency Rig:  Increases the output per cycle of your extraction.  More or less a mandatory rig.

Compared With old mechanics moons are receiving roughly a 50% boost in output per moon per hour.  Though this is dependent on the quality of the moon in the old system and the rate of refinery you use to refine the ore.

this brings this post to a close for now, i may add on to it, but ive run out of steam for the moment.  Add correct at will.