I am someone who “consumes” most bottles over two days, and most often attempts to taste and “analyze” them the morning of the second day. For the wines I drink, the large majority of the wines, both red and white seem “better” on day 2, especially the white wines, which are more consistent. I suppose , to use the OP term, “they are better in a different way”…a more matured aspect, showing their age and potential better.
But, I can’t really generalize or extrapolate from my experiences , as there are too many variables with others’ wines: age, type, treatment after opening, attempts at “preserving” vs. just leaving the wine in bottle to develop.
I mainly consume red Burgs from 15-30 years old; white Burgs(including much Chablis) from 10-20+; Alsace whites at 10-15+ and Piemonte wines. If I have time with reds, I always clean them of sediment and openly aerate them or “double decant” them and put them back in the bottle…if I don’t have time to fully aerate or don’t think the wine would benefit. (I don’t “pop and pour” or “pop” and “slow ox”, as I think “slow ox” does nothing beyond “pop and pour”. I think pop and pour will give the wine the least shot at showing well on day 1…and the best shot at showing well on days thereafter.) I always openly aerate whites, as I think they can always benefit. (Though I don’t do much with Bordeaux these days, most I open are at least 20 years old; they are often better the next day, for me, too.)
The next day (or after), I am looking for a more harmonious wine, consistent with good aging. If that happens, with good fruit remaining, and a more expressive nose/palate…that’s “improvement” to me.
Usually day 2 is when they show best for me, though some whites are even better on day 3. (I’ve found reds usually are less good on day 3. )
Beyond this, there are too many variables and definitions/criteria to generalize, I think. But, I am not trying to preserve or protect (from oxygen) the wines the next day, but to see how they evolve. I equate that evolution with aging potential remaining. I also think most of the wines I drink have aging potential beyond what I had ever thought; I’ve almost never had a wine that I thought was “too old”. (The premox is a separate issue; they were too old way too early on.)
enuff rambling