Hey Paul.
You may have already made a decision on this but I'm just now seeing this thread.
As long as you feel confident in your grafting abilities, my opinion/recommendation would be to graft. As long as you have the rootstock to work with that is. As Francisco mentioned, grafting onto a robust rootstock will give you your best chances. Especially if you have just a single piece of a rare cutting.
As Pino mentioned, timing is important too. I recommend grafting early in the growing season. It seems to be a little different with figs though. I'd venture to say that grafting can be done on figs just about any time during a growth flush. Still, I've done most of my grafting in early spring just when my fig trees are beginning to take off. I've have very good success during this time.
I recently paid a fair amount for a single rare cutting. I wouldn't dare take a chance just rooting it. If it dies on me without rooting, that's it, I'd have to buy another cutting. On the other hand, if I can get 5 grafts out of that one piece, I've just greatly increased my odds of establishing that variety in my collection. So, for me, It's an easy choice when I have a limited amount of a rare variety.
As for the practice of grafting on to a cutting and then trying to root that cutting? This is a practice that makes no sense to me if you have rootstock available to graft on to. Following this method might only marginally increase your odds by grafting on to a large cutting that may or may not have extra energy reserves. Still, not worth the risk to me as long as I have a root base to graft to.
By the way. My preferred methods of grafting have been the cleft graft and the saddle graft. Both have worked quite well for me. I personally, have had no success with chip or T budding. I know those have worked for others though.
Hope this helps.