When I worked for a couple of years for a business that made dining tables, coffee tables, entertainment units and such things, we used PVA almost all of the time.
If the faces being glued are a good fit, the join is stronger than the surrounding timber.
One advantage polyurethane has over PVA is gap filling, but there were no gaps to fill with the things we were building. My recollection was that we just tried the polyurethane as as experiment, but found it offered no advantage.
I build strip built kayaks and fit a laminated external stem on the bow and stern. That may be similar to what you plan to do. The laminations are usually about three or four layers of 3mm Jarrah. I just use PVA. One difference is that the whole kayak has a fibreglass skin inside and out, but I'm convinced that the PVA would hold without the glass.
Bow.jpg
If you are confident that the layers won't have any gaps at all, then the PVA would do the job. If you can't get a really good match between the laminations, then polyurethane may be better.
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