Except that's where the parallel falls through. The Hartnell crew had an old man, a young girl, and two middle-aged adults. Here we have three youngsters and someone who's old but seems almost as young. This actually wouldn't be a problem if it weren't for the fact that writer Terence Dudley seems to have given the three companions the most broad of characterizations. He's read that Tegan is bossy, Nyssa is smart, and Adric is chauvinistic (for some reason -- he never seemed to feel that way before), and so that's what the actors get to work with. Sarah Sutton comes off the best because she's sussed that if she plays the lines with a hint of detached amusement then it'll work out. Janet Fielding has to spend all her time complaining (mainly about how the Doctor didn't take her back to Heathrow and that she doesn't like Monarch's spaceship), and Matthew Waterhouse comes off the worst because his lines are all designed to make him sound like a stuck-up, awful brat, and he's not experienced enough of an actor (to put it kindly) to play against them. This is therefore really where the rot starts to set in for Adric -- when it was just him and Tom Baker he could play the bright-eyed inquisitive, but now he has to fight for attention between two other companions, one of whom has been written in much the same way as Adric had been. Adding two other TARDIS crewmembers was probably the worst thing to happen to Adric's character, and it's sadly not going to get much better. It doesn't help that Tegan and Adric don't seem to like each other very much.
Four to Doomsday is actually the first story filmed for the new TARDIS team, and you can sort of see it in Davison's performance. He's energetically enthusiastic about everything, particularly in the first episode, and even his voice is at a higher pitch than it generally is. But it's nice to see such ebullience -- makes everything seem more exciting, somehow.
The actual story in these first two episodes is rather slight -- we're as much in the dark as to Monarch's intentions as the Doctor is. But the exploration of the ship is quite nice, and the slow revelation as to the nature of the humans inhabiting it is built up well. Oh, and apparently Tegan is an accomplished draftswoman, with some really well done sketches as to what the well-dressed early 80s couple is wearing. Less plausible is her ability to speak the dialect that the aborigine Kurkutji is speaking118. However, as the rest of the story so far has been quite charming, we can forgive this. And it's a great cliffhanger for part two, as Bigon the Athenian lifts up his face to reveal that he's a robot, and then pulls out a small circuit board from his chest. "This is me," he says solemnly. Of course, we're not really any nearer to understanding what's going on on this ship (beyond the idea that Monarch wants to take 3 billion of his fellow Urbankans to make a home on Earth); maybe we'll get some answers next time.
118 In the 1980s there were around 200 different Aboriginal dialects still in existence (according to Ethnologue), most of which only had a relative handful of speakers. Even if we assume that she got lucky and Kurkutji spoke one of the more widespread dialects, like Warlpiri, there's still the matter of how Kurkutji (we later learn) is from roughly 33000 BC, so he should be unintelligible anyway (by way of comparison, only about 1000 years separates Modern English from Old English, and that's still largely unintelligible to current English speakers).
But then, even from an internal logic point-of-view, this gets weirder when you think about it; on a ship full of Greeks, Mayans, Aborigines, Chinese, and Urbankans, only Kurkutji is singled out as requiring a translator. So either the TARDIS translator is able to translate all the other languages on board except this particular one, or everyone else is speaking English and Kurkutji just refuses to conform. Except that everyone presumably understood everyone else before the TARDIS arrived, so they must be speaking some sort of common tongue that the TARDIS is translating anyway. Unless Urbankan is remarkably similar to English.