I'll be building in northern Michigan zone 6.   I'll be doing double stud walls with sheathing on the outer face of the inner wall,probably 7/16" OSB, possibly 3/8" plywood detailed as primary air barrier. 

My question is how vapor permeable should the primary air barrier be?
I plan on it being detailed with a liquid system.  Available permeability ranges from 0.1 perm (STO Vaporshield) to aboyt 10 perms (STO Emerald Guard. 

My rim joist will have a vapor barrier by a strip of EDPM roofing under the outer sill plate up & over the rim joist (supported by inner basement stud wall) onto the sub floor under the inner wall's plate.

The exterior will be 1/2" plywood treated with a liquid vapor permeable WRB probably STO Emeralg Guard covered by Greenguard DC14 XPS drainage plane covered by Ambrico EZWall adhered masonry (thin brick).
Insulation in the 'service cavity will be r15 mineral wool bats. 
The outer wall (55% 2x6 & 45% 2x4) & inter wall cavity, always 3 1/2," will be insulated with TBD.  The TBD includes blown in fiberglass, dense pack cellulose or mineral wool bats. 
My framing fractions range from 9% on 2x4 walls with no windows to 35% on a  2x6 wall that's mostly windows. 
My whole house wall r  (including rim joist) will be about r42 with the  "all" mineral wool option.  I haven't calculated it with the other choices but guess right around r40.

If I understand this correctly, the primary air barrier is something like 1/3 of the R value from the interior? That would put it at an ideal location for a vapor barrier, since it would always be above the interior dew point in winter (presuming you keep it 30-35% RH @ 68-70F in winter), and always below the outdoor dew point in summer in your location. You could then make the interior finish wall as vapor-open as you like, and it would have no associated moisture accumulation on the cold side of the assembly in winter.

In summer the (purpose designed) 1.1 perm Greenguard DC14 would be enough to protect from sun-on-wet masonry drives yet allow plenty of drying capacity from the primary air-barrier outward.

Be sure to caulk/foam under all sill plates (and between any double-plates). Using 1-part foam or construction adhesive under the edges of the plywood/OSB between the sheet-goods and framing is also recommended for both the exterior sheathing and the air barrier.

Figuring out in advance the continuity details of the primary air barrier in the walls with that of the floor, ceilings, windows, etc. can also relieve a lot of field head scratching and "Hail Mary" remediation. The EPDM strip works to get that continuity at the floor and to the basement walls, but note that with EPDM on the exterior of the band joist you'll have to use something low-perm like 2" of 2lb foam to insulate the interior side of the band joist or it could load up with moisture, since it will dwell at temps below the interior dew point for months on end in winter.

Dana1,
Thank you! I take it this means I should use the low permeability VaporShield.
OR? If I caulk the perimeter of each sheet of the OSB to the wall framework (including window openings), caulk the bottom plate to the EDPM, caulk the top plate to the ceiling OSB and caulk all inner wall corners. Doesn't the OSB itself without any "liquid WRB" become a 'smart retarder' & air barrier? The caulk of choice is acoustic sealant?

Also I anticipated the rim joist problem with foam & had planned to use r 15 mineral wool bats on the inside of the rim board. Also the coldest part of the rim board will have r12 between it and the cold concrete & it's only r3.5 (the thickness of the bat but the conductivity of wood) from indoor temperature so I should never have condensation on the rim board. I have a nice sketch of the wall cross section showing the rim board detail but it is to big to attach the scanned file.

A pure guess is that where it can be used, tape will outperform caulk. Consider multiple air barriers.

Jonr,
I wonder why you think tape will outperform acoustic sealant which is forever flexible and adheres, forever, better than nearly any tape?  Also, I do believe both Dana1 and I are not thinking of caulk applied after but having each sheet placed on a bead of sealant then nailed to the studs & plates.   As to multiple air barriers I will have a secondary air barrier, with 8-10 perms, by the exterior sheathing with liquid WRB.

Tape is seamless and can survive large movements. Caulk depends more on how well it is applied and can't tolerate much increase in gap if wood shrinks or twists. But it's just a guess and between two pieces of well secured wood, caulk may be better.

Tape requires a bonding surface to work- the liquid vapor retarders may or may not provide a suitable surface. The tried and true is still a bead of goop between the wooden sheathing and framing.

Acoustic sealant is cheap and remains pliable over time.

Low-expansion 1-part foam is also pretty cheap, somewhat flexible and bonds to wood well.

Construction adhesive bonds to wood VERY well, adding structural enhancement- the ply won't pop the nails and separate from the framing even in an earthquake.

Counting on OSB to be an adequate smart-retarder isn't a good idea in a place as cool as US zone 6. If you care enough to go for it, run a WUFI simulation of the stackup as a sanity check. A low-perm liquid vapor retarder 1/3 of the R out from the conditions side, and letting the outer 2/3 dry to the exterior, the inner 1/3 to the interior just works even on the napkin-math model, no simulation required.

Dana1,
Again thank you again for your sound advice! Vaporshield it is! I;ll use it on the OSB over the ceiling service cavity as well. I'll still need to watch indoor humidity when it's really cold outside for example 70f 40 % RH condensation possible in inner insulation if outdoor temp below -8f.
FWIW I've been thinking about the EDPM strip & how to make an air tight rim that is under the outer sill plate & under the inner wall's bottom plate with the vertical 6 3/4" step between the plates that covers the upper 1/2 of the rim board. With EDPM only "lapped" splices have any longevity ie no but joints. If a simple lapped joint is under a plate it creates an air leak. My solution is start with 21" wide strip all the way around the foundation made with all but joints. Cover each but joint with a strip that's 5 1/2" wide. Where each plate will sit, fill in between the joint covers with a strip the width of the plate either 3 1/2" or 5 1/2". The result is two layers everywhere under the plates & all joints in either layer lapped by the other layer. It'll be a cutting challenge as my foundation has 6 inside corners and 10 outsides.

With the,all be it small, possibility of wintertime condensation in my service cavity's insulation I'll abandon rock wool for that application, choosing cellulose or denim bats for the service cavity because they hold the water rather than drain it. I'm thinking it's less likely to create problems held in the insulation rather than wetting the bottom plate and possibly drywall. To get condensation in the outer insulation would take 90 degrees at 90 % RH with an indoor temp of 72f. Such outdoor conditions are extremely rare in all of Michigan and if they do occur it is not for very long. Also the exterior air barrier will work to make the insulation dew point an average of the the fluctuations in outdoor dew point .   In addition the exterior plywood is less vulnerable to occasional moistening than the drywall. In other words all the insulation options are ok in the outer cavities.

TAPE:
we're on our first project using European acrylic tape (Two suppliers - 475 high performance building supply; SIGNA). Vapor open, Passive House certified. Excellent product, nothing like it made in good ol USA. Expensive but worth it for first class results.