Most people don't understand what PPP means and the debate on the subject is often driven by ideology.
PPP effectively has nothing at all to do with whether the work is done by "the public sector" or a private company. Nearly all large infrastructural projects are completed by private companies but most are NOT done as a PPP. The only difference between a PPP project and a traditional tendering process is in the way a project is financed. The finance (i.e. borrowing) for an infrastructure project can come from the government or from a private company. If the latter is used, then it's considered a PPP.
Nor has PPP anything specifically to do with tolls. In many countries tolls are collected (and retained) by the government. You can have PPP built infrastructure without tolls or you can have publicly financed infrastructure with tolls.
There is simply no argument, in my mind, that having a private company do the work (assuming an open and competitive tendering process) is going to be more efficient that doing the work directly using government employees. However there is also no argument that using a PPP structure delivers far worse value to the public because the one thing the government of a stable country can do far more efficiently than any private company is borrow money. Typically the cost of capital for a private company currently lies within the range of 6-12% while I'd be surprised if the Irish government would have to pay more than a fraction above the ECB rate. Given that most PPPs run for 20 or 30 years, this roughly doubles the cost of the infrastructure.
In the UK, PPPs are getting more and more bad press as economists and the like are realising that the Enron-like accounting they represent is simply smoke and mirrors. While the initial cost seems less, all you are really doing is pushing the cost of projects into the future. It may seem great to get a telly on your credit card "for nothing" but if it takes you 10 years to pay off the bill then it will represent far worse value than paying for cash up front.