Gas turbines are more efficient in terms of size and weight for a given power level but burn more fuel. Merchant ships mostly care about fuel efficiency.

So why do power plants use gas turbines?

Do they? I thought most fossil-fueled power plants use coal, which they burn to power a steam turbine. Natural gas plants often use gas turbines, but this is very different from the gas turbine used by a ship: the latter burns kerosene, not natural gas. (Natural gas is uneconomical to power a moving vessel; because it's a gas, you need space to store it, and that space can be orders of magnitude bigger than an equivalent energy-density of diesel fuel or kerosene.) Diesel engines or oil-powered gas turbines are very rare for power plants, outside of backup generators for hospitals etc.

Peaking power. For the relatively short peaks when e.g. everyone gets off from work it's most efficient to fire up some gas turbines for a little while. Or on the relatively infrequent hottest days of the year.

Gas turbines are in fact used for direct electrical generation. In a combined cycle plant, the waste heat from the gas turbine exhaust is used to generate steam for a steam turbine.

For example: http://www.cpsenergy.com/services/natural_gas/natgas_generat...

Gas turbines are useful for peaking load, because they can be started and stopped quickly, relative to pure steam turbine generation.

A number of power plants in the U.S. generate electrical power by burning natural gas in a turbine.

Simple cycle gas turbines have efficiencies of 30-35%, whereas a large diesel engine can reach ~50%.

A combination of gas turbine, steam boiler running off GT exhaust and a steam turbine can reach efficiencies of ~55%. However, the system is complex and expensive, and not well suited for driving ship's propellers. Once additional kit like gearboxes are introduced, the drive system efficiency is no better than a direct-drive low speed diesel.

Finally, the diesel engines burn viscous, high-sulfur fuel... not really sure if a GT could handle the crap those engines use.