Here’s an anecdote.
My bias, fwiw, pretty perfectly aligns with what @SingKevin posted above.
Empirically however… I currently have two different jars of starter in my refrigerator. One of them is the descendent of the live starter that I originally got from Breadtopia in 2013 or 2014. The other one is a relatively new starter I created from scratch a few months ago as an experiment that I was walking through with @Fermentada when she was working on a chapter of their new sourdough cookbook.
Both of these starters are fed the same stuff (Breadtopia’s white bread flour) on the same neglected schedule and kept in small jars in my fridge.
Performance-wise they are interchangeable. They both leaven my dough pretty much the same.
Flavor-wise, in breads baked with them, there has been a subtle but reliable difference between them. Breads leavened with the Breadtopia starter have a somewhat richer, more complex flavor than the breads leavened with the newly created starter. Myself and Mrs. Homebreadbaker prefer the former to the latter (in her case, these were blind taste tests that I’ve conducted by not telling her which starter I used with a given loaf and in every case she has been able to tell me which one it was).
If you’ve read any of the posts I’ve put up here, or follow my instagram, you’ll know that I use very tiny amounts of starter in my bread - more of an inoculation than an ingredient. So I feel pretty confident in saying that the flavor difference that I am noticing between the two starters has to be microbial and not… ingrediential.
But the full story is still evolving and actually a bit more nuanced than the above. The way I maintain my starters is different from most conventional wisdom. I neglect / starve them in the fridge for long periods. It’s always more than a month, sometimes two or three months, between feedings. A lot of people would look at my starters and think they were “dead” (they’re not).
I have read that starving starter cultures like that over time exerts a selective pressure on the microbial populations, and that makes sense to the biologist in me. Any sustained systemic environmental effect would favor some populations over others.
The Breadtopia starter has been “starving” in my refrigerator for years and I assume that is partially responsible for the makeup of its current microbial population. The new starter is relatively fresh by comparison. BUT, it is now something like eight months old and I have noticed that over time it is developing more and more of the flavor character of the Breadtopia starter. At first the difference between them was very pronounced. Now it is almost un-detectable (I haven’t done the blind taste test with Mrs. H lately, but I’d bet she’d fail it now).
Since the new starter was created with, and always fed, the same white bread flour and same spring water as the Breadtopia starter, and also created in the same environment (in my house) where the Breadtopia starter lives, its flavor character can’t be only the result of the microbes in the grain / flour. My working hypothesis is that a good part of the flavor character I am noticing has to do with the environmental conditions over time (months of time).
Anyway, this is pure 1-trial anecdote and nothing like a proper experimental protocol. So your mileage will almost certainly vary.