I think one issue with the core being a [] and a winding/bobbin on each " [ " will be that the magnetic path will be reduced as compared to an E-I configuration where the entire winding is on a section that is ~2x the outside loop (the visible part of the lams) or in ascii: [ | ]
the " | " has to be twice the thickness of each "[" to properly pass the flux.
On the "box" core the flux is limited to the path that is visible - so as long as the xfmr is designed with a primary on one leg and a secondary on the other, ur good to go. But if you put a primary and a secondary on each leg, the flux carrying capability simply needs to be taken into account, and rated or "derated" so that the core is not saturated. (I'm just assuming/thinking here that one could sit oversized windings on this core, that might exceed the core's flux capability)
But assuming the cores are big enough, then not an issue anyhow.
Depending on the geometry one may or may not get a bigger winding window...
Nothing prevents anyone from using an EI core with windings on the outside legs, and not the inside...?
A possible advantage for the two bobbin/two leg arrangement might be that the windings and so the DCR of the two bobbins will be exactly the same for each half. A disadvantage might be that the two halves are separated by time via the lams, and at high freqs the hysterisis may mess with the HF response and/or create phase shifts - not sure on this tho'. Assuming application as a mod iron.
But for power, seems to me that you could wind the primary on one leg and the secondary on the other, done. Look ma, almost no special insulating techniques needed!
The other thing is that you could wind identical windings on each leg, and parallel the primaries - this would have the nice advantage of making the primary wire thinner per bobbin than with a single bobbin. Or you could play with this and series the primaries making the voltage per primary lower... or the same sort of deal with the secondaries...
Thinking about this makes my head go like this ---->
booga booga...
_-_-WBear2GCR