Digital Foundry shared some impressions they had of the Bioshock Collection shown off at this years Gamescom and they were mostly happy with the demo. The first two games run well on Xbox One & PS4, maintaining a 1080p resolution but have mild slowdown & screen tearing. One plus is that the physics systems that the original Bioshock have benefits from a higher frame rate, with that running in 60FPS; that wasn’t the case in the PC version of the original even if you ran that at higher frame rates than the console versions (30FPS).
Infinite looks to be a solid port too, with it largely being a new release of the PC build running at higher settings. We will likely hear more close to the collections launch but the first impressions are solid so far and the issues presented now will hopefully be fixed when it releases later this year.