Okay throwing in my two cents, for what it's worth...
I don't think it's in any way questionable that Peter Capaldi is hugely successful as the Doctor. The evidence is everywhere. Like them or not, both Series 8 and Series 9 have been on the favourable side of critical responses. There's plenty who dislike, and there's those who will now use the argument of comparison to earlier series as justification for their dislike, but there's also an incredible amount of praise heaped on the show as well.
So the show looks to have lost around a million viewers. Any show that lasts nine series (noted I'm not even counting Classic Who here) in the first place is considered a massive success. One that lasts that long and can boast that it's only lost a small fraction of its average viewership is mightily impressive. Better still, the show performs more than fantastically on catch-up services. When you account for the very obvious drop caused by the later scheduling since midway through Series 8 which correlates perfectly with a decline (people seem to pin the decline on Series 9, but it actually happened mid-S8 and there were a few anomalous drops in early Series 9 as a result of the Rugby World Cup and later on also Halloween), the show is still very much in rude health. When you consider that the show can generate enough interest to even contemplate a spin-off (even with fans as cynical as they are), it's doing considerably well. When it can trend worldwide because its lead writer is stepping down, it's something of a big deal. When a supporting character like River Song trends worldwide on Twitter, Tumblr, Facebook and whatever else just because they've announced she's coming back for a single episode you know it's doing considerably well. When Jenna Coleman leaves and 'Jenna' and 'Clara' both trend, is that the relative obscurity of the show? Or 'Capaldi' after the superb Heaven Sent was broadcast? Is this both a show with struggling popularity and worryingly declining figures also the same show that can sell out a venue like Wembley in London when they decide to host a celebration of the shows score music? That's something most Hollywood films aren't even given!
The argument goes that the show is still considerably important and popular for as long as its capable of generating headlines about viewer rating crises, and behind-the-scenes turmoil. As long as it's doing that, which it still is, it's an indication of mainstream interest. And as the face of Doctor Who, Peter Capaldi is currently the one who shares in some of the credit for that.
RTD had a hard job of picking up a show off the ground that was seen by many as a joke by the late Eighties. He brought it back admirably. Moffat, and I'm hardly his biggest fan, has similarly done an admirable job - a considerably harder job. Sustaining interest can be a lot harder than generating it in the first place. He played the heartthrob card with David Tennant and it paid off. The guy (for reasons I don't quite get myself, but each to their own) is a pin-up kind of guy. Combine him with the also rather popular John Barrowman as they did, and you have a time when the show had a distinct sense of vanity to it. Would Series 2-4 with the same stories have been as successful had Eccleston or Matt Smith led them? And on the flip side is David Tennant actually a comfortably better actor than any of the others? Subjective as it is, I think the answer is simply that he was an attractive lead, with an attractive companion and it played into the hands of mainstream viewers brilliantly. And then we realise that the mixed-reception to Voyage of the Damned doesn't correlate with the fact that it remains the most viewed episode of the last decade. A gain of hell knows how many millions of viewers for that special was no indication that the episode, its quality or indeed its reception was actually through the roof as well. So a decline of even a million on average overall across a decade is certainly no indication of quality or fan approval.
When it comes to awards, I think it's genuinely a great shame that Capaldi remains overlooked. I've more or less enjoyed the show consistently since it came back (Series 7 was a struggle at times) but can concede it isn't always award-worthy stuff. But Series 9, and 8 to an extent, both have moments or whole episodes where Peter Capaldi has shined. Again that's all opinion, but his efforts with Heaven Sent were probably the most worthwhile thing on TV for me last year. A lack of recognition for it is sad, but does not taint how much I loved it, or indeed how popular it was as a whole - it's already considered one of the best episodes of the past ten years. IMDB ranks it as the second best after Blink, whilst its top ten episodes are rather neatly divided with five RTD-era episodes and five Moffat-era episodes.
More on topic it is great that Michelle Gomez has been nominated for an award though. She's made me actually interested in the character of the Master in a way that John Simm couldn't. I'd say Moffat is due credit for that as well. She simply lights up the screen and is so utterly unpredictable and superbly villainous that it's great to see her get some recognition for it. Hopefully come Series 10 Capaldi will have received some recognition for his efforts as well, as I personally think he's a truly remarkable Doctor and an ever-growing global audience would seem to agree.