Two things change, and only one of them is the tannin.
The aroma changes a lot. American oak (Quercus alba) carries several times more whisky lactone than French oak, which is the coconut, dill and sweet vanilla signature. French oak (Quercus petraea and robur) is lower in lactone and gives a finer, more spice-and-toast profile.
The tannin changes in the other direction. French oak is markedly richer in ellagitannins, the fraction that does the redox and structure work. American oak gives less of it.
So the practical rule we would suggest: choose the species for the aroma you want, then check whether you still have the structural contribution you need. A wine moving from French to American oak often loses ellagitannin without anyone noticing, because the aroma arrived and the conversation stopped there.
In our range the two axes are separate on purpose. The Primary Colors range covers both signatures, with #14 and #15 on the French side and #23 and #24 on the American side, and you can add ellagitannin independently with #10 or EBX 810 without touching the aroma. Finishing tannins and maturation
Why the lactone difference is so large. Beta-methyl-gamma-octalactone exists in wood as non-volatile precursors, mainly galloyl esters, released by hydrolysis during seasoning and toasting. Quercus alba holds far more of the cis isomer, which is the aromatically potent one, with a perception threshold in wine an order of magnitude below the trans form. That single compound accounts for most of what people mean when they say a wine smells American.
Why the ellagitannin difference goes the other way. Quercus petraea is the richest of the three in vescalagin, castalagin, grandinin and the roburins, with robur close behind and alba well below. This is a genuine species difference, not a cooperage effect, although grain and seasoning modulate it.
Grain and seasoning modulate both. Tight grain, from slow-grown trees, gives lower extractable phenolics per unit area and a slower release. Long open-air seasoning, two to three years, hydrolyses part of the ellagitannin fraction and softens the green, bitter notes that raw wood carries. A tight grain, long seasoned French oak and a wide grain, short seasoned one are further apart than French and American at the same specification.
And the practical consequence for a substitution. If you are replacing American barrels with a tannin, match the aroma with the American profiles and then decide separately how much ellagitannin the wine needs, because the barrel was giving you less of it than a French barrel would have. If you are replacing French barrels, the reverse: the aroma target is easier and the structural contribution is the one you must not lose.