I'm not sure about actual figures for the fuel consumption effects - just the principle I'm afraid. The laws of physics will dictate that if you push something like a stabilizer out into the otherwise smooth flow of water over the ship's hull it must increase the drag effect - indeed the forces generated by the vane as it moves in the flow are what causes the desired force couple which tends to stop the ship rolling. The same laws govern the fact that as you increase the ship's speed with the stabilizer out, the power required to push the vessel through the water goes up exponentially in proportion to the increase in speed.
The problem was that, in order for the stabilizer to work properly, the ship had to be going fast enough for the required effect to be generated. Often, when the sea was really rough, the ship would have to slow down so much to avoid damage from slamming into large waves that the stabilizers would not produce much correction anyway. Add this to the fact that they could only correct rolling, not pitching, and you can see that they were not always "helpful"
During the time I was on board - towards the end of the Steam era - fuel costs were becoming a huge issue for the ship's operation. I can remember being in charge of the bunkering operation on occasions where the ship was re-fuelled ready for the next main voyage and there was always a sense of real importance placed on making sure the figures balanced for what was ordered, purchased and eventually recorded as having been loaded on board.
The choice of port where the fuel would be bought was always based on cost as well as other factors such as range, etc. The usual ritual in New York, before a transatlantic, would be to load in the order of 1000 Tonnes of Bunker C - spread throughout the ship's various fuel storage tanks. This would allow the ship to make a return transatlantic to Southampton without re-fuelling because the New York price was far more favourable. A bit like us avoiding the motorway services because of the price!
Bunker C was, essentially, what was left from the process of refining oil for other fuels and products such as petrol, etc - but it was still a very expensive part of the ship's operation. It was the fuel of choice for most steamships because of the cost, but it had to be heated before it could be used and contained some pretty nasty elements as a result of concentration during the refining process.
In the late seventies the cost of fuel was starting to really bite and power plants which were designed to operate on what - at the time - was a cheap and plentiful resource were now beginning to be a bit of a cost liability. The efficiency of the old steam plant - or lack of it - was, I'm sure, one of the main reasons why the engines were replaced. This was partly due to its age - not just to the changing operating environment with respect to the design conditions.
The new diesel electric system would show large benefits in efficiency as well as flexibility. Efficiency in the design would have been far more important than when the steam plant was designed. This is not to say that they wouldn't have considered efficiency when the original plant was built, but this would have become far more of an issue as we moved into the era of spiralling energy costs.
It would still cost more to run with the stabilizers out though!
