A mini split will be substantially cheaper to install, and once installed, will be a lot less likely to suffer efficiency losses due to leaky ducts, and long duct runs. The inverter style mini splits are super efficient, in "cruise" they can burn about 200 watts of electricity just chugging away. The way the inverter mini splits work is that they turn on in low power when demand is low, and they just run a little faster when demand increases, rather than turn on, turn off like a conventional unit. That way you save the power that would be used by the inrush of current starting and stopping the compressor. They are wicked efficient. I installed a 22 seer unit , a single 24k, at my old house in the great room, and it cooled the whole house and was stupid cheap to run. Might need a fan to blow air into a bedroom or something but generally the air circulated itself.
Pro installers seem to really hate mini splits, personally I think they are seeing the potential income from installation of all that ductwork going out the window.