It absolutley always does. If you raise the OD, you raise the gearing and you DECREASE brake power and unless you lower the car back again , you raise CoG whitch reduces cornering power and increases load transfer forward under braking. If you lower to compensate, you still have taller gearing and reduced brake power, plus now you have reduced suspension travel and suspension geometry operating away from the design point. No worries, now we fit bigger brakes and do a whole bunch of serious changes to get suspension geometric control back - oh and we probably need to some work on steering along the way.
In summary, unless you are talking doing all the downstream changes, don't change the OD.. If we are talking race - all bets off cos you need to change everything anyway
And... wide tyres come with increased sensitivity to dynamic camber change and the contact patch aspect ratio also makes them more skittish in response to road irregularities and more prone to aquaplanning and and and. But hey, have fun!