I have an Ergo, Babyhawk (toddlerhawk) and Beco Butterfly so I can compare how compact the three are.
The Beco rolls up a bit smaller than the ergo, I think it helps that it has special straps to contain it because it's really not that much less bulky of a carrier, IMO.
The babyhawk can be rolled up neatly by folding the headrest beforehand and tying the straps, so it ends up being the smallest of the three. I can throw it in my larger diaperbag with no problem-- it's long though and can't be folded length-wise because of how still the headrest area is, or at least I am afraid to permanently crease it.
I've never used a Kozy mei tai but my guess would be that it's even more compact than a babyhawk because it doesn't have a headrest... but I honestly don't know the thickness of the material/straps so I could be wrong.
I have a ellaroo original mei tai that folds up super small. The material is all pretty thin, including the straps (they have no real padding) so it is by far the most compact, two shouldered carrier I have. That said, it lacks any kind of head support and isn't as comfy for longer carries with my kid -- but he's almost 2 and is pretty dang heavy.
