You don't want a stiff one to be well hung on a balanced lug: you can go harder and faster with a floppy one so long as its well held.
Dad had carbon spars on his balanced lug rigged 12ft Scow for racing. It was certainly lighter, but with the sail track and blocks and line etc it loses some significance, but it was lighter, which has its advantages raising and lowering, and while sailing. It had structural foam in the ends to seal it and then some mast plugs and kevlar spiral wrap in places to to keep the carbon in alignment and provide abrasion resistance where needed.Conventionally you want a stiff mast (the sail was designed for use with stiffer aluminium spars) as if it bends it reduces luff tension, as the distance from downhaul attachment to sail mast head block reduces a bit. All bad on a lug. But in practice he found the slightly soft carbon mast would bend outwards on the 'bad tack' in medium to heavy air (top was held with shrouds/ forestay) away from the sail before it went really stiff, leaving a unimpinged airflow over the sail luff and he could sail faster and higher in the races on that tack than other boats, into the lead and win races. Dad was adamant that it he was faster sailing along with his flopping out, that this was a bigger gain than the reduction in luff tension on a balanced lug. Others were too conservative to believe it but he had the trophies. I guess if you take it to the extreme you'd purposefully make it quite floppy (like windsurfer masts are), then pre tension it stiff like a bow with your downhaul (like windsurfers do) as you hang your lug sail from it (where the string would be on your bow and arrow). But it would be assymentric and look a little unusual (but you'd win races), and you have to have a boat/ sail plan that can accomodate shrouds/ forestay, and the lug still swing. They weren't windsurfer masts, they were 'proper' carbon/glass tubes from http://carbonfibretubes.co.uk/custom.html and cost quite a bit.
We worked out the weights, I think aluminium works out half the weight of solid wood, and carbon is half the weight of aluminium as a bare tube. I think for price aluminium is cheaper than wood, here in the UK and where the sweet spot is for price and performance. Being untapered though the tubes look less aesthetic than a tapered one at the mast head. Adding shrouds reduces the required mast dimension and saves weight too whatever the material. How stiff they are no doubt is also affected by how they laid up too and the fibres are orientated but you can also make your own carbon masts using a cheap aluminium tube as the mandrel and make it custom. http://www.devboats.co.uk/cherubweb/masts.htmEd