The thing that makes Martha Jones shine so much compared to other NewWho companions, to me at least, is how she was the only one to deal with her end-of-season menace without superpowers.
Rose took the power of the TARDIS, became a literal deus ex machina and solved everything in five minutes flat.
Donna accidentally took on the brainpower of the Doctor and solved everything in five minutes flat.
Amy had the power to reboot the universe and solved the problem of the Doctor not existing in five minutes flat.
Jack was a highly-trained Time Agent, even before he became immortal.
Rory also dies a lot, was an Auton and retains the memories of 2,000+ years experience.
River Song is a highly-trained child-soldier Time Baby.
Unlike most other companions, Martha had no extra-special powers beyond her own awesomeness. Her achievement was IMHO greater than the ones above because she did it solely on her own merit. It may have still only been five minutes flat onscreen, but unlike Rose, Donna and Amy all basically snapping their fingers and saying “because I say so, that’s why!” her part in the Master’s downfall was an entire year in the making. While her task was made easier (and by ‘easier’, I mean ‘slightly less impossible’) by the perception filter and Jack’s vortex manipulator, she still spent a year telling stories in a hellish, decimated dystopia of a world. She had to give her entire species hope and faith and never lose her own, while never knowing if her family and the Doctor were even ALIVE, let alone how they were. FOR A YEAR. And this was after two months of racist, classist, misogynist humiliations at Farringham AND supporting the Doctor’s arse in 1969 as well. And she does it all in style, then leaves the Doctor wanting more (finally). This is why Martha Jones is Made Of Win And Awesome.
(Also, it’s notable that the only other New-Who companion who gets no super-upgrades and must be content with being a Badass Normal is Mickey Smith, the other black companion.)
Very seconded.
(Although, does Wilf count as a Badass Normal? If so, that makes me feel better about that bit of subtext.)