Four To Doomsday almost seems like it wants to be the Fifth Doctor's era's answer to The Ark in Space, as both stories are set entirely on a space vessel/station that contain some of the last surviving humans, and both exclusively feature the TARDIS crew exploring said vessel/station in the opening minutes. (And judging by how far off The Doctor was from getting Tegan to Heathrow Airport, someone must have given that Helmic regulator a mighty twist once again).
While the magic and awe of Ark is almost completely absent in Doomsday (to be fair, both stories were going for vastly different moods), visually, both stories are equal. Tony Burrough's sets for the Urbankan spaceship are simply stunning in their scale, and some of the strongest spaceship sets the series have ever seen. Nicknamed "jigsaw sets", Burrough designed the elements of the sets to be able to fit into different combinations in order to produce different rooms. Every time there's a scene change, we're still looking at the same three or four walls. We just don't realize it.
One of the first scenes shot in Peter Davison's run as The Doctor were some of the first scenes shown in this episode, namely The Doctor's solo exploration of the laboratory. Even in that first scene, you can already tell the direction Davison's Doctor will take. He examines the equipment in Monarch's lab with the excitement of a teenager, yet admires it as something that he had once seen five hundred years previously. Davison completely embodies the notion of a old man in a young man's body (as opposed to Patrick Troughton, who, it could be said, was almost the exact opposite). It is utterly fascinating to see, for the first time, a young man in the role. We easily take this approach for granted these days, but back in 1982, the concept of a young Doctor was almost completely alien to viewer and producer alike.