rel[type=carriageway] does not seem to be widely adopted and I haven't heard of any software taking that into account. I'd rather put the tag explicitly to avoid any confusion. 

Also, if marking the entire relation rather than individual ways is the preferred way of mapping dual carriageways, it should be reflected on the relevant wiki page: https://wiki.openstreetmap.org/wiki/Tag:dual_carriageway%3Dyes