[Update] Square Enix has provided an official comment on the matter to IGN, confirming both versions will run at 30 frames-per-second.
Both platforms offer the same outstanding Tomb Raider experience. Delivering the core Tomb Raider gameplay at native 1080p and running at 30fps was always our primary goal given the type of experience Tomb Raider is and the exploration we want players to do. Anything beyond 30fps for this version is gravy.
[Original] Tomb Raider: Definitive Edition will reportedly run at a buttery smooth 60 frames-per-second on PlayStation 4, and a lower frame-rate for those playing on Xbox One.
During a recent livestream with GamesRadar, Scot Amos, the game's executive producer, discussed the Tomb Raider's performance on PS4, saying, "Looking here, this is the PS4 version running at 60fps, again at 1080p. That's awesome for that to be able to showcase because when you get your hands on it you can feel it."
However, last week, Amos told Eurogamer that the game would run at 30fps on both Xbox One and PS4, but apparently now it is no longer locked at that frame-rate, with 30fps being the minimum. "The original goal for us, looking at both next-gen consoles... our minimum target was always gameplay front-to-back being 1080p and frame-rate 30fps," he explained.
A third report comes from Rocket Chainsaw, who apparently has insider knowledge of the game's performance. The outlet claims that the PS4 will run at an average of 60 frames-per-second, while the Xbox One port will run at 30fps, with the ability to move up to 45fps when less is happening on-screen.
While it appears we still don't have a definitive answer on the game's performance, it sure sounds like the PlayStation 4 version is the way to go.