I agree directly to ATO is best for privacy but as the third party business model is based on a fee from the employer they have some incentive to maintain privacy.
For cost using Manager existing solution is far less than your accountant or developing another integration.
For complexity outsourcing is probably easiest however setting up STP is not difficult.
Edit
For (an old) pricing comparison see Single Touch Payroll Australia - #68 by Patch
For the current list of options see https://softwaredevelopers.ato.gov.au/product-register