IMO (might be wrong), it's not debatable mate - this is one aspect where Stones is much superior - bordering on exceptional. Laporte is probably the more rounded defender of the two right now; and a good passer for the most part; but he has a propensity to panic on the ball when pressed high, and even though he is good at bringing the ball out from the back - his distribution and choice of passes is quite inconsistent. He can look good when he has space and time to think with serenity, but once you close him down, he goes turtle mode quite frequently - and dumps it to people (mostly Balenziaga, Iturraspe, Beñat) than try to navigate out of traffic.
Stones is much better builder from the back, and more consistent when it comes to picking out passes for his midfielders/ forwards; he's more mobile, and almost never loses his cool - which is a rather special quality in a ball-playing defender because even though he'll make errors from time to time (like young Ramos or Piqué), he's fearless and won't dwell on the mistake for too long. When he's pressed, he doesn't panic and always tries to make space for himself by a deft touch than just pass it to the nearest player (which can halt the momentum of the buildup).
Maybe it's a confidence thing with Laporte too, and it's mostly in his head; but he's distinctly weaker in this area than Stones - not just in terms of technique, but mental capacity and comfort on the ball. Then again, it's purely about degrees of aptitude - if we grade them on a scale. Laporte is quite proficient, but Stones is just majestic when it comes to distribution from the back and ease on the ball.
And yeah, totally agree with the last part, we need to sign one of these two because they're among the best young options on the market, and that might mean 3 positions in the back 4 sorted for the medium to long term depending on Darmian's development. If he doesn't improve, maybe we should sign Cancelo too, and really lay the foundations for an excellent young defense.