Can't talk about Big Island ukulele, except that I'd love to try one some time.
I do have a Keli'i Gold Series Tenor, and I love it. Some might say the neck is chunky, but I started out on (and still play) guitar, so the neck makes it easy for me to switch from one instrument to the other ... and the neck is still far less thick than one on any acoustic guitar I know of.
For me, the only minuses are that I'm not fond of the decal on the headstock (design is good, but the decal itself looks cheap-ish to my eyes), and there are minor (like, teensy-weensy) finish issues on mine; glue drops and stuff like that.
There is one wider issue as well. Keli'is are not completely made on O'ahu, although they were at one time. Part of the construction now happens in China (in a tiny shop, apparently, rather than a factory). Every vendor I've seen is totally upfront about this, but the luthier has not been equally forthcoming (label on mine says,"Handcrafted Ukuleles Made in Hawai'i"). Because of this, HMS no longer sells Keli'is. To be fair, it seems that most of the construction does take place on O'ahu -- which makes the label legal under the pertinent regulations. The fact that not many Keli'is are made per year would seem to bear out Keli'i's claims that they are handcrafted items made in small shops, with most of the build being done on O'ahu (and, I must add, in my hometown, although I have no connection with the luthier and, in fact, have never met him).
If you can get past these issues, the Gold Series are excellent all-koa ukulele that cost far less than their actual K-brand counterparts. (That said ... I swear I know a Kamaka when I hear one!)