I have the Laughlin 3k as well as the Martin 3K and the Kiwaya KMS-K, (Kiwaya's version of a 3K). In my opinion, they are all equal, but different. The Laughlin is a more accurate representation on a 1920 Martin 3K than the others. It even has bar fret wires. It is very open without being harsh and has good sustain for a soprano ukulele. If you didn't read the stamps you would probably think that it was a mint, early Martin, but with a cleaner build.
The Kiwaya looks more like a late 1940s Martin with the round fingerboard markers. It does not try to pass itself off for a Martin and has it's own style with the Kiwaya decal and small proportional differences. It is a little louder with a little less sustain than the Laughlin. Mine has a 1 piece top and back but regular production use 2 piece tops and backs.
The Martin 3K does not fit the question, but I am throwing it in anyway. The Martin is visually more bland than the others. The finish is more flat than satin and the rosette has fewer rings. The sound of this particular 3K seems to bridge the other 2. It is louder than the Laughlin and was better sustain than the Kiwaya. Fit and finish are nearly perfect and it is my personal favorite.
All 3 have their own unique voice and they all get played and enjoyed. There are times when I don't know which one I am playing. For me, the Laughlin is the coolest because it was hand made and mine is special with the kite and bow tie. The Kiwaya has beautiful wood and has a great classic look. The Martin has the name, build, history, playability and sound, and despite what I said earlier, looks very nice and is a new take on the early Martin without actually attempting to be a replica.
I highly recommend all 3 as well as the Kiwaya KTS-7, (Mahogany). They all play very well, look great and sound great to my ear. Strings make a big difference and I prefer the medium Worths, (high G), or the Martins. I am mostly a fingerstyle player, but all three play rhythm well too. For me, it is nice to be able to go back and forth between the Koa and Mahogany, (and my Cherry 3 too). My ear seems to get a little too used to one tone, so I have to wake it up I thank Martin for making an instrument that has been so lovingly copied.
I know that there has been some negativity posted regarding the recent Martins, but the ones that I own and love get the most play and are wonderful, (coming from a long guitar background), so please don't write them off. If I were to sell on the my Koa 3K type ukuleles, it would be the Kiwaya, so I guess that is where my opinion shows through. It is not a lesser instrument, it is just that it didn't come from Nazareth and it wasn't hand made in Carlsbad, so like in the past, my Harleys and Beetlecat, it does not invoke that sense of history with me, (it's all in my head of course).