Look at the "Limiteds" as simply another guitar flavor, but it's a seasonal flavor as opposed to one in the regular lineup found on any day over the counter.
Whether the factory ends up procuring through chance a nice "wood find," or simply deciding to delve into their limited stash of coveted special woods, they create a limited line that is, truly, limited in number by sheer virtue of the small/finite supply of that species. Sidebar: this is wholly different from "signature series" Limiteds where the number is held by purely arbitrary choice (witness Gibson, Fender, et.al.).
So in answer to the question of whether the Limiteds sonically live up to their aesthetics? The answer is definitely maybe!
It's a guitar with different top/b/s wood combinations, and often with build specs; thus it has to be judged as a different guitar. So whether that particular Ltd. floats your tonal boat really is as subjective a question as they come. Personally, I've played many a Ltd and felt they were "merely" another nice Taylor (ok, not a bad thing right?), but nuttin tonally special. Then there are my two personal favorite Ltd models (only one of which I own) that are tonal home runs. My opinion only, and so it goes.
FWIW, one thing the Ltd models do have in their favor is the factory bundles lots of nice features that, were you to add these up yourself, you'd pay considerably more. So assuming you like the tone of a given Ltd, it offers more bang-for-buck than a Modified/BTO'd version.
Edward