It is quite frankly amazing how good the dynamic is between the original TARDIS crew, and 'The Dead Planet' shows it to astonishing effect. Very little actually happens in the episode; the TARDIS lands on a strange planet, and the main characters wander around for a bit before reluctantly exploring the citadel they found earlier. But the episode isn't about where they've landed; it's about where they haven't landed. Ian and Barbara had their adventure with the cavemen, and now it's over and they're expecting to go home. Instead, the Doctor seems perfectly content to start another adventure right on the back of the first. And it's the rest of the cast's reactions that drive this episode and make it so incredible.
Every scene works because of the characters and the actors playing them. Susan does an excellent job of mediating between the Doctor's enthusiasm for exploration and the schoolteachers' desire to simply move on--her growing fear of the jungle, driven by her certainty that they are not alone, leads her to do what was unthinkable just four short episodes ago and side with the humans against the Doctor. Barbara is relentlessly pragmatic, attempting to find ways to reconcile the conflicts among the group simply because she recognizes that a bad situation won't be any better if they're all at each other's throats, no matter who's right. Ian slowly simmers, his frustration building as the Doctor's arrogance and obstinacy risks all their lives. And the Doctor, well...he's already driving the series. The look on Hartnell's face when he "reluctantly" concludes that the city is their only option to find mercury speaks volumes not just about the scene but about the whole character.
This is why the Aaru movie feels much longer, even though it's actually quite a bit shorter in terms of the running time. The plot beats are all the same, but the conflict that makes this such riveting television isn't to do with the plot. It's the characters. Frankly, the show is never going to be quite as good once Ian and Barbara leaves, simply because there's never going to be anyone who challenges the Doctor quite so credibly.