Under- and overrated is kind of hard to pinpoint when it isn’t related to something like a Doctor Who Magazine poll but more in regards to “the wider fandom”. It really depends on which corners of the internet you find yourself in.
Anyways: The Claws of Axos is massively underrated everywhere 
Count me in as a fan of “The Invisible Enemy”. It’s bonkers, but always fun. And, for me, episode 1 is genuinely very VERY good.
I think “Knock Knock” probably is underrated and love watching it with my headphones on. The sound is sumptuously good!
I agree that “The Tsuranga Conundrum” is underrated. It’s not perfect, but I don’t think it’s anywhere near as bad as many suggest. Always entertaining for me.
“The Claws of Axos” is a great story, but hugely ambitious. I give it credit for the ambition and adore the concept. I genuinely would love to see a modern take on the Axons, and the energy crisis elements (and patriotism threads) would gel well today.
I will have a good think for my own pitches for underrated stories… 
I love that one too. It’s creepy and David Suchet is so good as the Landlord.
Never understood the hate for this one myself. It’s a bit of an average story, but it’s definitely not as bad as the fandom would lead you to believe.
The P’ting are definitely one of the Chibnall era’s most iconic monsters, and you just know that Big Finish will probably throw them into a Classic Doctors, New Monsters set at some point. I’d love to hear the Fourth Doctor encounter the P’ting.
OK, so a classic story I believe to be underrated is “Frontier in Space”. It’s often seen as a runaround that features just an endless procession of the Doctor and Jo getting captured and locked up. Whilst I don’t deny that this happens (and quite a lot), it is also a hugely ambitious story with vast scope for the time in which it was made. It is replete with sumptuous world-building, the only TV story (so far) to feature the marvellous Draconians. It also explores issues of propaganda, truth distortion and fake news that are very much relevant today, explores the polarising effects of politics and popularism, suppression of the right to protest etc. It also showcases Jo Grant’s carefully developed character arc and personal development. It is very much a story with resonance for today, featuring the Master as an arch manipulator, Ogrons, Draconians, Daleks etc. I think is is often derided for the (admittedly) messy and confusing ending but even this would have made more sense had “Planet of the Daleks” been written more directly as a follow on instead of a classic Nation retread of his greatest hits.
“Frontier in Space”. I love it!
I just uploaded my old review of that one to this site, and I completely agree. It’s so underrated. Frontier In Space is an epic space opera that finishes Roger Delgado’s time as the Master in style.
It’s a real shame it was his last appearance though, because of his tragic death. He was taken from the world too soon.
Here’s an underrated story from each of the Classic Doctors in my humble opinion (apologies if these aren’t all as ‘underrated’ as others these are just stories I feel don’t get enough love or at least I dont see it)
Hartnell - ‘The Smugglers’
The Smugglers blew me away when I watched the reconstruction last year I found it to be an absolutely enthralling pirate tale with a delightful cast and a very satisfying story as well as a great introduction for Ben and Polly in their first TARDIS trip! - 8.5/10
Troughton - ‘The Krotons’
The Krotons is a story that I was shocked to find isn’t very loved in the fandom, I really enjoyed this story start to finish. It’s a harmless robot overlord controls colony storyline and I think the Krotons themselves are effective as villains. That paired with one of my all time favourite TARDIS teams gives me a story I can’t help but smile all the way through! - 7/10
Pertwee - ‘Death to the Daleks’
Death to the Daleks is a story that I thought was very creative in all honesty, yes it has the single silliest cliffhanger of all time with the infamous ‘stop don’t move’ * dramatic zoom at floor tiles * but honestly looking past that this is one of the first stories to do something wildly different with the Daleks putting them on the back foot not letting them immediately become the master race. I really enjoy this story from the city the exxilons themselves I think it all just works! - 9/10
T.Baker - ‘Revenge of the Cybermen’
Revenge is a story I can understand peoples dislike for, it portrays the Cybermen all types of wrong and to some is considered boring. I for one think it’s an awful lot of fun, not least because it features probably my actual favourite TARDIS team. The cybermat spreading the disease, Voga is believable at least to me and I as much as they’re portrayed as purely robots (the line from Baker when he says they’re complete machine creatures is terrible) I do thoroughly enjoy the Cybermen throughout this story. Overall an overlooked fun adventure - 8/10
Davison - ‘The King’s Demons’
The King’s Demons is a story that given its short run time is still spectacular effective in my opinion, you have Ainley being the delightful master he is and an actual sword fight as well. I find Turlough to be entreating in this story too as by the end of it he’s ready to have a fight with the entire castle which never fails to make me giggle. I adore the idea of Kamelion and it’s very unfortunate how all that turned out. The storyline with King John is shory but sweet and the only thing letting the story down is the somewhat rushed ending with the mind battle between the doctor and the master but is till thunk it works - 8/10
C.Baker - ‘The Two Doctors’
The Two Doctors is a wonderful story. I love the combination of characters here and think they all work beautifully together, my biggest complaint about this story is the lack of 6 and 2 actually interacting but that’s made up by the prominence of Jamie I think and the fact Troughton can always hold his own in every scene. The Androgums make for a great new villain and the return of the sontarans is always welcome in my eyes, this story also has some very dark moments which is a trademark of Season 22. Overall a fantastically fun story! - 8/10
McCoy - ‘Delta and the Bannermen’
I know there’s at least one user on here who will wholeheartedly agree with this one. This story is just so much fun from the Doctor to Ray it all just works. I think the bannermen are effectively goofy but dangerous villains, the queen and her child provide us something to root for and I desperately need to mention the two Americans who always provide amazing comedic moments. I also found myself genuinely shocked by story beats here especially when they explode the bus, it’s so dark but perfectly done. The only real issue I take with this story as well as much of season 24 is the fact Mel gets almost nothing to do which is a shame. But overall, this story is an absolute blast and is very underrated - 8/10
If I may nominate one from each Doctor… Well, most of them. 8 only has one (or two?) and I feel like 14 and 15 are still too fresh to say how the fan culture rates them, so:
1: The Savages
2: The Underwater Menace
3: Planet of the Daleks
4: The Pirate Planet
5: Frontios
6: Mark of the Rani
7: Delta and the Bannermen 
9: The Long Game
10: The Runaway Bride
11: The Rings of Akhaten
12: Hell Bent
13: Eve of the Daleks
Can confirm that I only started to like Gwen at all from watching this series, and I also think it’s very underrated! While not as consistent as Children of Earth, I think it actually goes harder in several places. I’d have loved more series of Torchwood after this continuing the trend from it and CoE of “deeply engaging with a central concept/premise in a way that explores how ■■■■■■ up humans and our systems can be”
I actually like the song! And yeah The Gunfighters is very much in my top tier of Hartnell stories, it’s brilliant. I also love Absolution and Colony in Space, although Colony I’ve seen enough people agree with me on that it’s not one that would’ve occurred to me to call underrated
Some stories I think are especially underrated: The Sensorites, The Space Museum, The Underwater Menace, The Space Pirates, Planet of the Daleks, The Monster of Peladon, The Power of Kroll, The Armageddon Factor, Meglos, Terminus, Planet of Fire, Timelash, Terror of the Vervoids, Delta and the Bannermen, Silver Nemesis, the TV Movie, The End of the World, The Long Game, The Battle of Ranskoor Av Kolos, and Orphan 55.
All of these stories I’d happily sit down to watch any day, and I’d happily call them all great (maybe apart from Timelash on the “great” front, although I do think it’s at a minimum “good”).
The Space Pirates… great?
I really enjoyed it!
That’s amazing to me, it is my most disliked classic serial by some way - I found little to no enjoyment throughout the whole story unfortunately
I’m a sucker for gradually exploring a setting and I loved that aspect of the story, the picture painted of that era of the future. Also Milo Clancy is funny and the model shots are chef’s kiss.
The model shots are the only redeeming factor for me, I unfortunately did not gel with Milo Clancy at all. I just felt the whole story was lacklustre that paired with the fact the main cast are barely in it I really didn’t like the serial as a whole
That’s fair!
I’d also suggest “Smile” is underrated. It’s not the best from series 10, but it is consistently interesting. I also like the sense to exploration from the first third of the story that feels very reminiscent of classic Who stories. These days, we are so often thrown right into the heart of the story so quickly that it is nice, occasionally, to come across a story that allows our understanding develop alongside that of the Doctor and companion. “Smile” does this very well. It’s light years ahead (in my opinion) of Cotrell-Boyce’s other DW script (the deeply frustrating “In the Forest of the Night”.
Yes, agree, Smile is actually a great episode and I’m always surprised it’s not more widely liked.
also seconding @DispersalPhase on The Space Museum and Silver Nemesis - Space Museum I genuinely love and again I was surprised that many people seem quite lukewarm about it, and Silver Nemesis… is it good? Maybe not. But it sure is a hell of a lot of fun