MIMF

What wood grain should you use for a guitar neck? Should it be flat or vetical grain, and what benefits do either cut bring?

If I'm reading this correctly, you'd be asking whether the board be flat or quarter sawn. Quarter sawn wood with the grain running vertically to the fretboard is the most popular choice but I've used flat sawn maple and mahogany with no ill effects and you tend to pay more for quarter sawn boards because its a less effecient way of harvesting wood. With a good quality and properly dried piece of lumber. I feel that there isn't a lot of value to the extra cost.

I often use off quarter wood for multiple part necks. That way you can arrange the grain to your advantage.

I see alot of advantages using vertical grain on the fretboard because it has better wearing properties, is stiffer and less likely to warp than flat grain. The guitars I have to look at all show flat grain, with either maple or rosewood fretboards, and frat grain again for any mohogany or maple necks. Why is that? Is it because they are not high end guitars?

vertical grain is not necessarily "stiffer and less likely to warp" than flat grain. It does move a bit less across the width of the neck, and the look may be preferred on an aesthetic basis.