"Short" answer: to me, it would depend on heigth settings under the strings in this case. A pickup with A2 set low enough to give similar Gauss readings from the strings should behave not too far from the same pickup set higher and with an A3 (minus the small differences due to a wee bit more iron / more inductance / more eddy currents with A3).
Side notes - I won't repeat my stance about the variability of discrete magnets including those of a "same" alloy, since I'm not even sure that such posts are read.
I'd still wonder to which extent we can generalize on this topic. When Throbak defines A2 as "mid scooped" while Seymour finds in it a "warm, sweet full tone", the explanation is not necessarily that one winder is wrong and the other right. ;-)
Anyway.
Below is a comparison involving various alloys including A2 and A3 among others, FWIW (the contributor talks about "AlNiCo 3" while there's no cobalt in A3 but beside this indifferent error, I find his test instructive regarding what magnets really do: when we talk a long time about them, it emphasizes their properties in a way not necessarily indicative of how tone actually changes or not).
EDIT - A few months ago, I had shared a chart showing what was objectively going on, EQ wise, with A3 vs A2 and A3 vs A5 in a same neck pickup, played direct to the board. I paste the related screenshot below. Left column stacks the frequencies and shows the output level with single notes. Right column does the same with chords from unfretted strings to 12th fret.
These results were predictible since they matched the variations of Gauss levels + inductivity measured on the pickup with the magnets involved.
