It would seem that not only is all matter the same for all transporters, so that a Federation machine, a Klingon machine and a Cardassian machine can all equally well dematerialize a Bolian - but also all phased
matter is the same, so that a Federation machine, a Klingon machine and a Cardassian machine can all equally well rematerialize a Bolian who was dematerialized by one of the other machines.
We see such "handover" of signal in several episodes, and in DS9 "Dramatis Personae" it is especially clearly shown, with a Klingon machine creating a Klingon pattern (red glow) and then blowing up; the phased matter stream remaining in limbo, and our heroes grabbing it with their Cardassian machine; and the transportee finally rematerializing out of a Cardassian pattern (amber glow). There was no careful synching of the two systems beforehand, but lots of effort after the crisis developed (after the Klingon machine blew up).
So, basically compatibility is 100% guaranteed, because a transportee is a transportee is a transportee, regardless of whether he has been dematerialized or not. One can even "intercept" or "steal" a matter stream, such as in TOS "Assignment: Earth". It's not a case of everything being lost if machine B doesn't instantaneously receive the signal handed over from machine A, but something way more robust.
This is why everyone seems to rematerialise with a visual effect appropriate to the transporter pad
There are cases where remat is appropriate for the receiving pad, and others where it is appropriate for the sending one. We can probably simply assume that the former happens when the receiving pad has been cued in advance, and actively contributes, gently easing the phased matter stream back into our realm, while the latter is just a case of the sender not bothering to inform the receiving end and merely treating the receiving pad as an inert target where the phased matter degrades back to normal matter on its own.
As for the "xerox and destroy vs. transform and move" argument, the former model is not supported by actual onscreen events or dialogue. It's just plausible speculation, rendered somewhat moot by the piles of explicit evidence for the latter model. Somehow, the transporter just changes matter into another form (phased matter), so that it becomes invisible, can go through walls, and can be shot across space, until it degrades back into normal matter at the destination, apparently without extra prompting. It seems that variations of this are seen in "The Next Phase"/"The Pegasus
" (where phasing creates the invisibility and the wall-penetrating ability but does not culminate in spontaneous rephasing) and perhaps also in "Time's Arrow" (where the two abilities again are witnessed, even if the mechanism involved is a tad different). Who knows, perhaps phasers (what a suggestive name!) are another application of this phasing technology, rendering the victim permanently
invisible and incapable of interacting with the normal universe?