I know nothing about American Originals, but the '63 AVRI Precision certainly has very different neck. 1.75" nut width for starters. Curved ("slab"?) fretboard. Manufacture of those necks would have been expensive for Fender.
Nut width of AV and AO P-basses is exactly the same (please check the specs).
Concerning round-lam vs. slab rosewood boards, Fender started transitioning towards round-lam boards in 1962, so the AV ‘63 P-bass is period-correct in this regard, but the AO ‘60s as well, if we want to be picky, since there’s no specific year of reference in the instrument’s name.
With regard to the relevant manufacturing costs, this is an old, useless and almost trolling topic that’s been dealt with many times without any conclusions.
In general, what Leo Fender did during his years at Fender, was to find ways to simplify and making the instruments’ manufacturing process the least expensive as his declared aim was to produce good quality tools for the largest amount of people.
In the case of the transition from slab to round-lam boards, however, there were users’ reports about lack of adherence between the rosewood board and the maple of the neck, which, sometimes, also prevented the truss-rod adjustment.
Fender thought that reducing the rosewood’s thickness could help in increasing the strain compatibility between the two kinds of wood; however, the first reduction step made necks more expensive as it wasn’t so significant, whereas the cost of carving the board to the desired radius was to be added.
Fender reduced the board to a veneer with a second step of the rosewood thickness reduction, which is what should characterise also the AV ‘63 P-basses.
This solution was continued for all rosewood-board Fender instrument’s up to 1983.
We can surely say than the AV ‘63 is P-bass is definitely a period-correct instrument, especially with regard to the fretboard radius.
Fender probably found that two different lines of fretboard preparation and manufacturing were now too expensive for non-Custom Shop instruments and likely decided to streamline its production processes.
As stated, however, it should be noted that in the ‘60s and ‘70s, all rosewood boards were round-lam, hence the production costs where to be spread over the whole production; this likely helped in keeping the cost down to acceptable levels in view of the company’s margin targets.
So keep your AV in good shape as they are true vintage-reproduction P-basses under all aspects.
I couldn’t buy one and went for the currently made line (AO ‘60s); frankly speaking I would have loved a board with a 7.25” radius but I couldn’t care less whether it is made of a thick slab or not in terms of bass tone or playability, even if I like the idea of having a largest reserve of noble wood in its neck as I saw round-lam vintage instruments where the board was almost completely gone.