R-Core Transformers

Power loss, EM interference, and probably some impedance and frequency response characteristics too (not sure about the last two)

In addition to the lower flux leakage as mentioned in this article, there is a benefit of R-core and toroidal transformers which is reduction in the strains due to magnetorestriction that happens, which is what can make transformers- especially cheaply made EI-core transformers- have "hum" at 2x the AC fundamental frequency (e.g. 100 or 120hz for mains powered devices).

Given your name, the practical answer is that there is no difference assuming they are properly selected and implemented in the circuit. The exception being the EI core and SE outputs, EI cores were the only ones made with airgaps last I was paying attention. Audio is just not as picky as some would like to make it out to be, sure a torroid in the power supply will let us get away with a more compact layout and make it easier to get the noise specs we want but it is not that difficult to do with an EI core. When you get down to it, they are each different in some vague but highly marketable way.

Edit: I am over simplifying things, there are differences but my point is that in audio work the design execution is what matters.

I thought it was going to be about implementing transformer models in a way that fits well with some special kind of hardware like those green arrays or whatever they are called (the low energy use, highly parallel (but maybe low clock speed?) ones)

I thought it was maybe something like: https://rpubs.com/eR_ic/transfoRmers becoming a core R package, and I was like, okay why?

Meanwhile, I was so happy to finally see an article about transformers that is really about transformers and not some programming thing.

Reactance is the only thing really limiting current flow in the primary...without it (which can be simulated by shorting the secondary) only the resistance of the wire would limit current flow. The subsequent joule heating of the transformer would result in thermal runaway without it.

The main advantage of this setup is to drastically reduce interwinding capacitance and DC leakage current.