The advantage it one continuous layer of foam, easier to install, no cutting and fitting, it leaves the bulk mass in side as a heat sink, it makes a thermal break where your studding will conduct cold, and as a solid sheet on the outside it acts as a better air barrier, air leakage is a major factor. On the cost side you will use less can spray foam.

Understanding you have 2xs on the flat you can fit additional foam in this space and dry wall over that. When you cut to fit foam into that space set the table saw at a slight angle so the foam wedge fits into the bay, tighter.

When heat sources come up I always think that wood is the simplest and cheapest as it has to possibility of "free" attached. When fossil based fuels come they can in no way be gained free. So I usually insert "use more fossil based foam" here, it is like purchasing your fuel once, just thinking longer term. You can really bake yourself in a wood heated space, so much so you may want to vent the building at times by opening a window.

How is the ceiling insulated?

When using vapor barriers you want to be careful that you don't use two, one inside and one outside where you could possible build up trapped moisture, it will leak and moisture will get into the space and it won't come out as easy as it goes in. I don't see where the system you are thinking of using acts in this way. The only place in question would be the ceiling.

Vapor starts to get complicated in the area of dew point and how much insulation you need to void this factor out so that moisture does not condense on the exterior face of any warm foam. 2" of foam is not enough to stop this. So on the outside the foam should be strapped and then the new siding added over the strapping giving it an air space to dry out. One more benefit to insulating outside the structure.