Differences: Fabric - not just the dye, but the natural indigo pair has a significantly more 'knobbly' aspect to the surface of the denim. It undulates. Fantastic, although this is not to everybody's tastes. It's also a thicker, stiffer denim, and hence less comfortable to wear. The crossroads where all the fabrics meet at the crotch is a particularly 'wodgey' area
The synthetic indigo denim is darker, still very slubby (not dissimilar to Warehouse Duck Diggers - another fantastic pair of jeans). Fitting is similar. Slim, '47 style fit. Front rise around 11". The naturals fit a little tighter in my experience - this may be due to the thicker fabric. The natural indigo's have thick thread stitching round the pockets, rise, J stitch and inside leg. The synthetics only use this thick thread on the lower rise and the top of the side seams. As stitching goes, I actually prefer the latter.