I think you're comparing apples to oranges, at best. Both woods can be
fine for a project, but they're completely different. Either will
warp, depending on the cut of the wood, knots etc... Both will cup &
twist, too. I'd have to say that I usually have better luck with
Yellow Pine, it's inherently more stable, being denser, with a longer
grain & is a lot stronger than White, so I'd use the dimensions that
you'll be cutting it to for making a decision. It can split easier
than the White, though. You're back to how the wood is cut & how
you're going to join it & at what dimensions.

Comparing either one to Red Oak or Maple is another kettle of fish.
They're hard woods, the first extremely ring porous & the other is
diffusely porous. All have completely different finishing properties.
How are you planning on finishing it?

Half the battle with any project is picking out the wood. I've gone
with a different species simply because I couldn't get enough of one to
be able to cut out enough good pieces for the amount of money I had to
spend or because the design called for strength that one wood had &
another didn't. Finishing is always a consideration. White Pine
blotches unless you seal it well before staining. Yellow can have
pockets of resin that won't take a stain well. Red Oak needs to be
filled while Maple is usually perfect for staining with almost no work.
Mostly, I like clear finishes because the wood is so pretty anyway.
If you're painting, who cares? You might as well use plastic wood.

Jim