Their strength is obviously part of many factors, also including a strong driver in Hamilton but also the engine. To how much, is anyone's guess, but I wouldn't bet against it being a significant factor.
Analysis of Melbourne showed that Ferrari were gaining on the straights and losing in the corners. The simple conclusion would be that Ferrari have a strong(er) engine and weaker car. A more realistic conclusion of that, is that it's not just about engine performance. It's just as much about fuel efficiency.
Post winter-testing, there was a strong belief that Ferrari's race simulation was compromised by a necessity to conserve fuel. Since then, there have been various reports that indeed Mercedes have probably the most efficient engine coupled with perhaps the most powerful one too. This allows them a significant advantage on a few fronts: They can utilize that by starting with less fuel, or at the same fuel can retain more power longer. Or both, at the same time. Either is significant. Less fuel offers an advantage that the car is lighter which has a positive effect on cornering speed, acceleration but also tire wear. From all reports by Ferrari and RedBull, this advantage in fuel efficiency isn't insignificant.
Coming to Melbourne which is in the top 3 of most fuel heavy circuits, all indications are that Ferrari chose to run a low(er) downforce set-up to minimize drag and minimize fuel consumption. This compromised their cornering speed, which fits the qualifying analysis perfectly of the Ferrari gaining on the straights but losing significantly in the corners.
So yes, a lot succeeds and falls on the engine. To how much extent that engine is responsible for the teams success is anyone's guess, but it is a major contribution. No doubt the car/chassis/aero is good too, but without having the ability to compare these different teams with the same engine, it's impossible to say how much the other factors contribute and perform against one another.