C...I am watching this post because I think it is a good question! My instincts tell me you really need a rootstock that is at least 3-4 times larger...in order to have a decent cambium layer contact.BTW...have you read on the cloudforrest forums how many people claim these bark grafts are extremely weak unions and often break off after obtaining some size??? That worries me. I would like to hear from others who have had successful bark grafts that last.

I have bark grafts on European plum that grew 8' in one season last year and none of them broke in spite of some strong winds in the fall.

Floyd:

Years ago I did many bark grafts each year on upright junipers (not fruit trees). I say many as I did these commercially and the nursery I was at did about 5000 each year.

I just want to say that we used rootstock at least equal in diameter to the scion or bigger than the scion. Smaller
diameter than the scion did not work.

How much bigger? It has been a long time since I bark
grafted but I would say we used rootstocks up to twice
as wide as the scion and did just fine. Did the bigger
rootstocks result in better success? No. The results
really depended on the skill of the grafter, how well the
cambium layers matched up, freshness of the scions ect.

I do recall the wider rootstocks were a bit easier to work with. I presume the same situation would apple bark grafting fruit trees.

The few times I have done simple bark grafts with calipers close....I really did not like the result. They took, but the resulting graft was lumpy with minimal cambium contact...the geometry of the small radius/small radius fights you. I was not impressed with the vigor of the takes or it's first season healing/strength.

I feel it works much better when the understock is 2X larger or better.

When working in the same or near same caliper, there are a number of better (but more complex) bark grafts...saddle, strap, ect...That I believe are both stronger and faster to completely heal over.
Konrad has posted (on gardenweb) a nice technique for bark grafting material of pretty close size...but I believe even his example was probably 1.5X the scion.

If the diameters are very close, why not do a whip and tongue?

I have done a lot of bark grafts and found them to be effective on smaller diameter rootstock up to 1.5 inches. I have lost quite a few to birds and wind in the first 2 seasons. For more matching diameters I am going to start using saddle grafts. They are stronger since they are centered on the rootstock and double sided. About as simple as a bark graft there are numerous tutorials on You-tube. On very large base diameters I find the cleft graft to be the very best.

If you are bench grafting I probably wouldn't even consider bark grafting. The bark grafts I described were top working.

1 year bark graft on apple:
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1 year whip and tongue on apple:
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2 one year bark grafts on plum:
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Murky, to try to answer your question, I am generally more comfortable with whip and tongue grafting, but my understanding is that there's potential for significantly better percentage takes with bark grafts with some species even apart from diameter ratio considerations. Besides wanting to escape the limitations of matching diameters, I'd like to explore options for improving my grafting success rate with various non-pomes. I'm hoping that various types of bark grafts will increase my success rate with pawpaws, persimmons, and maybe mulberries, and perhaps also work better for species I'd like to begin grafting like pecans, walnuts, and stone fruit. I experimented quite a bit with the modified method of bark grafting from David Osborn's online tutorial (particularly for persimmons) last year, but I've only just started trying more standard bark grafts, and my first impression has been that the cambial contact I had envisioned with a simple bark graft isn't realized very well unless the stock is at least 2-3 times the diameter of the scion. Bill Reid on his pecan blog describes three types of bark grafts he uses according to diameter ratios, starting on the smallest diameter stocks with 3-flap grafts, then using what he calls an arrowhead graft (which seems like the most basic bark graft), and then using what he just calls a bark graft (but involves several angles and asymmetries) on larger stocks. I don't know how applicable those ideas would be to other species, and I'm also curious how others might approach things differently.