Well, we knew this would happen - well at least I did - and here we are, Fallout 4 is experiencing performance problems on the Xbox One and PS4. Users are reporting that the frame rate drops to well below 30FPS, even when there's no on-screen action.
One user 'Kenzodielocke' reported that on his PS4 the game "has massive problems holding the 30fps when inside buildings, cages or whatever you have a load time when you get in". He continued: "This get's way worse when people shoot at you or throw molotow cocktails. I am no technical expert, but I think this game might be locking itself like The Witcher 3 did. Firefights in buildings feel exactly like fights in The Witcher 3 in the swamp when it's raining. In the open world the game has hiccups too, but not as bad as in buildings. This just isn't fun, when you can't even aim properly because of the frame rate".
The thread on NeoGAF is huge, so feel free to read through it for more people complaining about the performance and FPS in Fallout 4. There are people without problems, but it seems like even with the day one patch, performance issues are there.