We've done both for years, but prefer Tusker House...since it is a buffet it has more of a variety and plenty of choices for everyone (including carved meats, Krispy Kreme donuts and unique offerings including AWESOME fruit breads).
They both have P.O.G. juice (it's the Lilikoi juice from Kona at 'Ohana), my kids LOVE that juice...and so do I! As far as characters, both have Mickey then 'Ohana has Lilo, Stich & Pluto while TH has Donald, Dasiy & Goofy.
Like other's have mentioned, you may just want to go to whichever fits better into your agenda for the day, both are good character breakfasts...but out of the two, we just enjoy TH a little more. Good luck!