White Elmers is "Aromatic" PVA, Yellow is "Aliphatic" PVA.
The two terms refer to the bond linking of the polymer chains.

I have always worked on the principle that as long as the glue is sronger than the material it is gluing - it is strong enough. Try using the glue to join two bits of the material and when it is properly cured - pull the joint apart and see what gives - the glue or the wood. If it is the wood - then the glue is adequate. - NOW FOR THE DISCLAIMERS

Chemical resistance also plays part - that is one of the reasons for Epoxy anywhere near an Engine bay and why I wouldn't use personally use aromatic PVA on a float plane (Water resistance).

As has also been very well stated - Joint design and fit is also important. How many firewalls do we build where pretty much the entire glued joint is under tension? Such as the ones where there is a bit of Tri Stock Behind the firewall onto the flush cut fuselage sides? - in those cases you want a glue with good tensile strength (usually we use epoxy for that reason too). If the glued area is only under shear or even better - compression - then the glue can be just about anything as long as it is as strong or stronger than the material being glued.

Then there is fatigue resistance of the glue to consider too.

I have had this argument with some of the ARF manufacturers when I have seen weaknesses in their design coupled with the glue used.