Goose,
Did a taste-off for you!
Both have similar characteristic Laphroaig character.
The Quarter Cask to me has a little sweeter note to it (even though it hasn't spent any time in sherry casks) at the front, and is definitely a more full-bodied scotch. Has a sort of oilier, more viscous, richer mouthfeel and taste to it.
The Triple Wood is more woody/oaky, and maybe a touch astringent. Definitely a drier feel to it. A little more spiciness, and some sweetness on the back end. Maybe overall little more complex flavors than the Quarter Cask.
I definitely prefer the Quarter Cask, simply because IMO the wood overpowers the other flavors in the Triple Wood.