The Build engine didn't use BSP, it treated connections between sectors as portals and rasterized the walls as (90 degree rotated) trapezoids while performing clipping against those portals. This allowed it to have dynamic wall geometry (e.g. moving trains, rotating light fixtures, etc) as well as "room-over-room" setups as long as you couldn't see both rooms at the same time (in both Blood and Shadow Warrior they found a workaround for it allowing to create more "3D" spaces by making identically shaped sectors with the floor of one sector acting as a portal to the ceiling of the other sector - supposedly this wasn't "natively" supported by the engine, but it was flexible enough for the game studios who used it -without even having access to the source- to do it themselves).
The first level of Duke Nukem 3D does use a few Build tricks - e.g. another one is that sprites can be "axis aligned" instead of following the camera and they can also have collision - this can be used to create rudimentary 3D geometry by treating each sprite as an axis aligned quad and in the first level it is used to make a bridge between two buildings (right before the level exit button).
Blake Stone Rise of the Triad used later versions of the Wolf3D engine and had textured floors/ceilings
> Doom and IIRC Duke Nukem as well used a BSP engine which was much more flexible
Duke Nukem (Build engine) did not use BSP