TripView is the best if you are wanting to obtain real time information, such as when the next bus/train.ferry is, however the Transport Infoline app (the one provided by TfNSW is the best when it comes to planning ahead.
It works in the same way that the 131 500 website works, namely you can input your starting point (and you can stipulate current location using GPS if you want), end destination, and it will work it all out for you (e.g. "Walk 100 metres to bus stop, catch route 999 bus to location X, walk 30 metres, catch train from platform 1 to location Y, walk 40 metres, catch ferry from wharf 3 to location Z, walk 40 metres, catch bus 998 to destination") - TripView doesn't do that.
The 131500 app also lets youdo a search based on either departure or arrival time, so if you need to be somewhere by a certain time, it will work it out for you.
FWIW, I have both TripView (and I agree, get the paid version) and the Transport InfoLine apps on my phone, they are both worth having.