In my experience they turn the trip off.

You can still be awake, but you won’t be tripping any more, the sleep only comes if you actually lay down and try to go to sleep or take a large enough dose of benzos.

They dampen the effects and quell the anxiety, and depending on what stage of the trip you're in and how hard you're tripping they may effectively kill it entirely. I would take a bit of valium on the tail end of a trip to sleep or quiet my brain as it reconstituted itself after being atomized into the cosmos. I only took benzos once during the upward trajectory of a trip near the peak, after suffering physical panic symptoms from a strong batch of wild-picked wavy caps (first and only time I've felt physically threatened by a psychedelic). It didn't kill the trip, but it killed the panic and allowed me to enjoy the experience.

Bit of both but more the latter.