Who is the lead? Doctor or Companion?

I think it really depends on the story. For instance, Rose is absolutely the lead in Rose, but the Doctor is the lead in Boom Town. Other times it's hard to say who has the A-plot and who has the B.

Although I'd say over the 55 years, there have probably been more stories where the Doctor is the lead.

Heck, there are stories with no companion at all (The Deadly Assassin, Valhalla, Dark Horizons...) - and stories where neither the Doctor or the companion is the main protagonist (Blink, Who Killed Kennedy, The Flywheel Revolution...).

So yeah, I'd say it's a case by case basis, but both are absolutely important. Just depends on the story you want to tell.

The Doctor is the lead. Having a show with someone else's perspective doesn't make that person the lead.

I’d argue that the lead changes from episode to episode as unlike a movie where you kind of have to have one protagonist, each episode is essentially its own story so we’ll get episode where the lead is the Doctor, the companion, both, or occasionally neither.

It's Doctor Who; the character of 'The Doctor' - or 'Doctor Who' if you prefer - is the leading role by definition. Seeing stories through the perspective of the companion, or any other character, doesn't make that the leading role in the show itself.

I'd argue that the Doctor is the lead and always has been. However, in this modern age where viewing television has become a complex task more akin to reading a really long book, it makes sense to have the lead character be a part of an ensemble. If you look at the evolution of Star Trek, the Classic series featured Kirk and his two co-stars Spock and McCoy with several supporting characters. As the movies developed from that series the co-stars began to take more part in the stories which reached a peak in 3 and 4 where they were contributing as much to the story - almost - as Kirk, Spock and McCoy. This led to TNG where there was a lead - Picard - but an equally important ensemble of characters who had just as much development and backstory as he did. Follow this through to DS9 and Voyager in which Sisko and Janeway were nominally the main characters by virtue of their command positions but were not the main focus of the series.

Or look at Buffy The Vampire Slayer: she's the main character but there are times when other characters play a larger part than she does. It doesn't invalidate her role as main/ title character, it just reinforces the other characters.

Doctor Who is still Doctor Who. But the supporting character - the co-lead who also has their name in the credits as a main character - also has a big part to play in the success of the show. If Doctor Who has changed focus on its characters - and I'd argue that the role of companion is still essentially the same as it ever was - I'd argue that it's because the nature of television has changed.

I'm in the co-lead camp. The best Doctor and companion teams tend to share whatever story their experiencing, each character complementing the other. Outside of the ones already mentioned, I very keenly remember one scene from Pyramids of Mars with the Fourth Doctor and Sarah:
A large part of what made that team so good were that they acted as foils to one another. The differences in one always revealed something meaningful about the other. Sarah's horror reveals the Doctor compassion, the Doctor's coldness reveals her loyalty.

And we tend to feel it when either party are given the short end of the stick. There's a very discernible absence. The Sixth Doctor and Peri's dynamic on audio clips along in a way that it was never really allowed to on television. Both are given something to do and allowed to spark off each other and those around them. Same is true of the Seventh Doctor and Mel. It's that line from way back in The Edge of Destruction: "We learn about each other, so we learn about ourselves."