Despite notable improvements over the initial demo code, Final Fantasy XIII on PlayStation 3 still had a few performance weaknesses in its final Japanese retail rendition and these have been carried over to the UK launch code too. The Crystal Tools engine seems to have issues rendering several characters simultaneously, especially if the protagonists are close-up when presumably the highest LOD models are being displayed. Additionally, the full-resolution alpha buffers used for the likes of particle effects could also cause issues - pretty impactful in the demo code, much improved in the retail release.
We previously speculated that this would be less of an issue on the Xbox 360 and it turns out we were right. But of course, bearing in mind the big resolution reduction, if there wasn't some kind of performance benefit, we'd be pretty shocked.
Frame-rate analysis shows that while both games can lose performance, it's the Xbox 360 version that runs smoother in like-for-like situations. However, the advantage - such as it is - is minimal during gameplay.