I’ve heard Doctor Who described as a “children’s show”, but it seems a bit violent for that at times. I would describe it as equivalent to American sci fi shows like Star Trek, Farscape, Stargate SG-1, or Firefly. Basically “adventure serial” sci fi. Most of the time, it’s not taken as seriously as some of the events might suggest, except when it is:
Chris Eccleston’s doctor was dealing with a lot of PTSD from the events and his actions in the “Time War” that kind of defined his character throughout his run.
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This clip from Classic Who is probably one of the few times I can remember a companion (Tegan with the Fifth Doctor) showing that it might not actually be “fun” dropping out of space and time into the middle of various interstellar wars and meeting new and interesting people minutes before they are murdered by Daleks, Cybermen, Sontarans, or some other monster of the week. If you think about it, traveling with the Doctor actually sounds pretty freakin terrifying!