Dear Michal,
ticket sales are under precise inspection due to loses generated by uncomplete integration. Integrated tickets (subscriptions actually) are bit cheaper than normal tickets - if you are travelling more than 40 trips per month (counted 20 days from home to work and back). Difference is not big, because this is not the target of integrated system to be cheap, but to be systematic and offer more connections for same value. If you travel more (there is no trip limitation, just date limitation of subscription), is more cheaper for you as traveller.
Authority for regional buses is region (Bratislava region self-government), but they are connected with the operator.