The ZIP wall system sheathing very air tight at least initially. I'm not super-confident in 100 year air-sealing performance of any tape though. But with a foam-over with staggered seams the consequences of brittle tape or compromised tape adhesives are of little consequence. To use it as a weather resistant barrier you have to take care not to ding it up during construction, and detail the seams (and window & door flashing) appropriately.
Open cell foam air-seals measurably better than cellulose, but cellulose has more stable R value over temperature, and unlike foam, can buffer much of the wintertime moisture load, protecting the wood, and it has a modest amount of thermal mass, whereas o.c. foam has almost none. With caulk or construction adhesive or 1-part foam at every interface between the framing & sheathing cellulose walls are every bit as tight as o.c. foam walls. Sealing between doubled-plates and between the bottom plate & subfloor with a bead of caulk or adhesive is an important air-sealing detail whatever you do for cavity fill. The thermal performance difference between o.c. foam and damp-sprayed mid-density cellulose is "in the noise"- the care & quality of installation trumps insulation type. Costs are often comparable, but that's very much local-market driven. With 2" of insulating sheathing on the exterior the annual humidity cycling that drives settling of cellulose in walls is much reduced, and the adhesives in damp-sprayed goods also resist settling. Dry-blown you'd probably need to hit at least 3lbs density to eliminate long-term settling, which may cost more than open cell foam.
A rainscreen limits bulk water penetrations, and enhances the ability of the wall to dry toward the exterior, unless the rigid-foam layer has a highly vapor retardent facer (like alumunimum foil), and allows the siding to dry quickly. While it's greatest benefit is in rainy coastal wind-driven areas (like coastal British Columbia, where it's required by code), it's of benefit in any cold climate where moisture accumulation in structural sheathings are an issue. In US climate zone 5 the rainscreen-enhanced ability to dry toward the exterior removes the requirement for a class-II or -I interior vapor retarder, even without exterior foam:
http://www.buildingscience.com/documents/guides-and-manuals/irc-faqs/irc-faq-insulating-sheathing-vapor-retarder-requirements
With exterior foam secured by furring (attached with pancake head timber screws 24" o.c. penetrating into the studs) the rainscreen gap is ready-made, and using it as such is easier than not.
Without exterior foam a 2x4 wall is pretty low-performance for a zone-5 climate, but with a couple inches of foam it's pretty good, typically in the ~R20 whole-wall range.
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