That's a quaint way of putting things, but... While Takhisis and Paladine are based on Tiamat and Bahamut, respectively, (or at least on their unnamed original incarnations in OD&D), the lore was different (at the time of DL's inception, there was very little lore on Tiamat and Bahamut—a lot of what we have came later) and abilities do differ (different statblocks, greater deity vs. lesser deity, etc.), and effort was made to made them distinct and grander. DL also assumed a different (if minimally explained) cosmology than the Great Wheel.
So, this retoconning (that apparently started with 1e's Manual of the Planes) to them being the same entity probably feels irritating after all the lore and effort the original DL team put into making them distinct.
Frankly, the power-level difference never mattered to me; they're gods. That said, in 4e, Bahamut and Tiamat are both essentially "greater" deities by the usual classification. By which I mean, 4e doesn't
make this distinction. There are gods--male and female, as "goddess" was considered an unnecessary relic of gender-enforced terminology--and there are beings that are less than gods but still divine, such as exarchs and angels. Further, in general, Bahamut and Tiamat have been gaining power over time, and I would argue no small part of that is the depiction of the pantheon-leading five-headed color-coded Evil Queen of Dragons and Tyranny and the one-headed platinum-scaled Good King of Dragons and Heroes as seen in Dragonlance. In which case, one could argue that the comparison would be better phrased as, "
Tiamat is Takhisis." It's just that Tiamat's name is more widely-known, because (as noted below) it's more widely
used, mostly due to being in the public domain.
Couldn't give two figs about the Great Wheel cosmology. More importantly, it's clear Bahamut and Tiamat don't either. They're actively part of the Great Wheel, the World Tree, Dragonlance, Eberron (though at a distance removed, as with all gods in that setting), the World Axis (as noted above), and others as well. Same for Tiamat. The siblings are no provincial backwater gods, they're all over the place.
Your statements about "all the lore and effort that went into making them distinct" sound like someone trying to cleave apart "well sure, aesthetically, philosophically, and behaviorally they're identical, but in
this cosmology there's a whole bunch of history that isn't relevant in any of the others." And I grant that. That doesn't stop them from being multiple
incarnations of the same fundamental core. To be clear, I
like having multiple incarnations of a common core. I think that's really cool. As I said, I have my own names for slight variations on them (and Io) meant to serve as publishable names in the unlikely event that I ever actually did publish (better to have, and get comfortable, with non-infringing names
now so that there can't be any reluctance in ten years when theoretical future me is looking for a publisher.)
Ultimately, it just feels like a really weird insistence that no, Takhisis ABSOLUTELY CAN'T "just" be Tiamat. She ABSOLUTELY MUST be an Original Character Do Not Steal. The sentiment is silly. There is no shame in Takhisis being Tiamat (or Tiamat being Takhisis, if you prefer that ordering.) If anything, it proves that for all the flak Dragonlance takes for enforcing railroading on the game and overwrought plots etc. etc., it has an unambiguous and enduring legacy: Dragons, dragon gods, dragon
people, etc. all grew
specifically because Dragonlance left a permanent, positive mark on the growth of D&D.
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