I'll take a stab at this question.

GRAFTING:
In my very limited experience, if you are starting from a healthy, fresh cutting, it's almost a sure thing to graft a tip from it to either a seedling rootstock or an already-rooted cutting of another variety. It can be done with a minimal amount of skill, provided you have the right tools. I think it 'takes' to the rootstock and begins to grow more quickly than waiting for a cutting to root.

ROOTING:
As for rooting cuttings, I can tell you I've lost a lot of cuttings to rot over the last 5 years because of overly wet, or too cold conditions, or who knows what reason. And some varieties are reported to be harder to root.

Growers also say that some varieties just don't do as well on their own roots (as a rooted cutting). But I have no experience to back that up. Also, when you graft, you only need a 3 or 4 inch cutting (if that much). So you're not sacrificing lots of limbs of your prized tree in order to propagate it.

I'm sure others will want to comment. I'll be interested in what they say.

Dave-in-Nova Thanks for that.I can now see the principle that some stock may have a more vigorous root system than the one to be grafted to it.I presume that the cutting to be grafted must be more desirable because you must sacrifice the stock plants own system in order to sustain the new one.Is that a fair comment?

Yes, generally named varieties are more valuable -- at least from an economical perspective. If, for example, you purchased a 'Lava Flow' cutting on E-bay for $60 (yes, that's about what Lava Flow cuttings are going for!) and you've tried to root it, but for some reason it's failing. The bottom is getting soft and the middle is getting squishy. I'd be very tempted at this point to sacrifice a generic yellow plumeria as rootstock (easy to start these from cuttings), and graft what's left of the healthy tip of the 'Lava Flow' onto the yellow. I'm trying to keep a number of rooted yellows just for that reason.

Oh, one more drawback to grafting is sometimes the rootstock will 'outgrow' -- that is, in diameter -- the scion (grafted piece) and it will just not look very good long-term (though it's still a very healthy plant). But then, I suppose you could either plant the whole plant deeper, covering and hiding the undesirably ugly graft union, or you could air-layer the now-growing 'Lava Flow' and grow it on its own roots.