I shall quote my pal Karl Hoyt herewith:
"...when wood is harvested, it is either sliced right straight through the log flat sawn) or cut into quarters and then cut into boards so that the grain runs vertically through the board.
A flat sawn board will have grain lines that look like a smile, a quarter
sawn board will have grain lines that run vertically (or nearly vertically)
The reason for the board to be quarter sawn is to give the board stability
and strength (and in some cases it shows off more interesting features......
curly maple looks best on the quarter while quilted figure tends to be more
brilliant when flatsawn) . A quarter sawn board will not twist and warp as
bad as a flatsawn board. if you look at a flat sawn board after it has air
dried for a while, the board will often develop some cupping or twisting as
the wood dries out etc., So in theory, a quarter sawn neck (or body) will
not warp or twist like a flatsawn neck might and is a tiny bit stronger.
HOWEVER>>>>> if we are talking about well seasoned maple, ash, walnut, or
other relatively stable hardwood, this is not a significant problem. When
I build my 10-15 basses a year, I can take the time to find boards whose
grain is really nice, but there are thousands upon thousands of flatsawn
necks out there built by factories as well as custom bulders which have
withstood the test of time and the rigors of bass and guitar playing without
problems. As long as the wood is properly seasoned when built with, the neck
will in all likelihood be stable, especially since it will be sealed with
finish of some kind."