I have 3 of these in my house very similar to the first one. 2 of them are in my living room (under windows so they double as a window perch), another upstairs in a spare bedroom with another litter box in that room. What I couldn't tell about the first one is how the lid is opened - mine are on long hinges so they simply open up - you don't have to lift them off and move them - I suspect the lid would be heavy if it is wood.
When I had one of them in a room by itself, we did occasionally have the litter box wars. Once I moved it to a room with another, there is no more competition.
They will trap smell inside only if you don't clean the walls and underneath the box. The first one (like mine) has a plastic type coated wall that is VERY easy to clean. The third one looks great but the wood will absorb the smell and you will never get it out - had an unlined wood one once for about 6 months and had to pitch it due to the odor.
I also place a throw rug under the litter box and a tracking mat in front between the box and the hole. The rug is pulled out and washed on a regular basis and it also protects the floor from litter that is flung out of the box during burying. The tracking mat is dumped out each time we scoop.
If your cats are not used to covered litter boxes, these may threaten them. Before you invest in any of them, make sure they are OK with a covered litter box.
Here are pictures of mine: