I own and have played lots of vintage Martin's, and I've also played all of the different Kiwaya soprano models (several ukes of each model), and none of them sound anything like a Martin - they're nice, but not at all like a Martin. If you're looking for a vintage Martin type sound, then I would NOT consider a Kiwaya. They don't have that brash, barking, LOUD sound full of overtones that my Martin's all seem to have. The Kiwaya's just do not have the richness that is at the same time very very punchy, that my Martin's have (though the Kiwaya's can be punchy - but they have a dry sound without those Martin overtones!!!). Mind you, I have 2 Kiwaya's that are keepers, as well as one that I'm letting go of. But they are not Martin's or even Martin-ish.
I have also played one new Martin S-0 and it also had a completely different kind of tone than a vintage Martin. It was also on the quiet side. It also felt heavier than my vintage ones.
To tell you the truth, the nearest new uke I've tried that had a Martinish tone was a cheapo Ohana mahogany soprano made in China... Nope it wasn't a Martin, but it was kinda Martin-ish. I almost bought it because of that, but then I thought, that's dumb... I already have the real thing... But that little Ohana was real punchy, had a lot of volume, and sounded rich too. Might have been that particular one, but I thought it was a real deal and a steal!
There are also other kinds of "vintage" tone besides the Martin sound. Martin's aren't the only ukes that have been around the block. Hawaiian made ukes from the teens and 20's do not sound like Martin's, in my experience!!!! They are also very very loud, but a real different kind of tone. Thes old Hawaiian ones don't have a raised fretboard and that limits the tonal palette, and control over the tone and volume (at least with my mediocre playing skills!!).
Honestly, I prefer more modern sounds, so now I have one mahogany 1920's Martin, one soild koa Kumalae from the 1910's, one solid mahogany unlabelled soprano from the 1960's (because it was my first ukulele), and all the rest in my uke herd are modern ukes that are not at all vintage sounding! And to be truthful, I don't play my vintage ones except the Martin at xmas time - I like to play Christmas carols on it because you can hear it so extrememly well over everyone's singing! And because it's my tradition and everyone expects it...
One of my best buddies, on the other hand, only plays his old Martin - because that's what a ukulele is supposed to sound like... well duh, he says!
And you know, everyone's ears are different. We hear and like the same things differently!