Sustainability is a complex thing, not least because there are a lot of different meanings attached to it. This question goes into that a little more. So unless you define what you mean by "sustainable" people won't know. Is it just greenwash "sustainable coal power" or is it 100% recycleable, or what?
The EarthBag website talks about about LEEDs characteristics
My reading of it is that table 1 is the key summary, and I've copied that here for when that link breaks. The LEED system evaluates a house on a list of criteria and the table lists those and describes how the house fulfils each one. A lot of those criteria may not matter to you, but they're key to some people's definitions of sustainable so they are in there. You can ignore them.
Taking the first item "ND Neighbourhood" they summarise that as "promote responsible land development" which they differentiate from the next item "avoid environmentally sensitive areas" so I take that to be talking about social sustainability rather than ecological. In other words, this is about not going into a poor/affordable neighbourhood and buying a house there that you're going to knock down and replace with a much more expensive one (gentrification). They're achieving that via "design decisions" which I assume means "not buying a site in a poor neighbourhood".
That goes for every point on the list, but because LEED is a proprietary system you need to pay to get access to the details. That IMO makes it less useful as only the people who pay know what it means. By using it you're saying "I'm sustainable, but I'm not going to tell you any details". If a major corporation said that would you believe them?
How does barbed wire compare to steel rebar, and how do the quantities (or weights) compare with similar square footage?
I think it would be extremely hard to use the same weight of barbed wire as a concrete house would use steel reinforcing, I'd expect 1/10th or less weight of wire. And it's weight that matters here. As well, and probably more important, making the cement in the concrete uses huge amounts of energy where the adobe house uses little to no cement.
How sustainable are polypropylene bags?
They're not. But in many ways that's the wrong question. Two more important questions are: where do the bags come from?; and what's the alternative? From the link:
typically burlap or polypropylene feed sacks in 50 or 100 pound sizes
That looks as though they're reusing bags that would otherwise be sent to landfill or if we're lucky, recycled. Reuse is better.
What's the alternative? Pure adobe houses take skill to build and have limited ability to withstand rain, so they're not suitable for all locations. Using bags like this probably enhances their rain-resistance and also lowers the skill level required of the builder. They're also fairly slow to build unless you have a solid stream of hot days for several months while building. The bag system doesn't require that.
Other alternatives are rammed earth and (sundried) mud bricks, which like adobe requires formwork and sun. The EarthShip tyure system is more labour-intensive and uses tyres. Tyres have more material in them than bags, so are less sustainable there, but are also harder to recycle and thus more likely to end up stored rather than recycled. But it's also much harder to build a whole house from tyres, so EarthShips inevitably have a lot of non-tyre structure (and the labour cost means they often only have a "feature wall" of tyres)
On balance I'd say the bag system is better.