Those are the two major types of tuners available on Ukes.
Friction tuners (as you are already experiencing) stretch the strings way more than Geared tuners. One tiny turn, and boom - you're a whole semitone up.
Friction tuners are the more traditional ones (I think) and some people prefer that look.
Advantage of Friction Tuners:
Weigh Less, don't portrude out of the headstock.
KenMiddleton often says that Friction tuners reduce the weight of the head of the instrument, making it easier to hold.
Disadvantage of Friction Tuners:
They are more difficult to tune with, since they change the pitch of the strings by a lot with only a little bit of turning.
Geared tuners have cog wheels that turn with the peg, allowing for the pitch of the strings to be adjusted at a slower ratio. They can either be sealed (covered up) or open (you can actually see the cog wheels).
Advantage: Generally easier and more convenient to tune with.
Disadvantage: Added weight.
Personally I would go with the sealed gear tuners.
I have both types and find the Geared much more convenient and easier to tune. The Friction tuners always get on my nerves, because I'm impatient.
But it's all a matter of preference
Congrads on getting the Mainland.
I have heard GREAT things about them.
I was wanting to get one as well (as a poor student), but couldn't afford it. Hopefully in the future sometime