Compared to electrification, gas turbines lack the ability: to localise (or even completely get rid of) emissions, to provide regenerative braking, and they take up additional space onboard. They have much the same sort of advantages and disadvantages compared to electrification as a Diesel powered train.
So it then boils down to Diesel v Gas Turbine. The Gas turbine generally has a better power to weight ratio, requires less lubrication, and is physically smaller than an equivalent ICE. However, they only work well at a narrow range of speeds and loads and aren't very good elsewhere, which makes them fairly good for boats and power stations where it'll be operating at optimum parameters for days on end, but not good for trains where it has to keep on jumping around for every PSR, restrictive signal aspect, etc. Additionally, all the space saved by having a smaller power unit would be quickly lost to the increased space needed to store the fuel, and not to mention that a gas turbine is going to be far more expensive than an equivalent powered Diesel engine.
I'm also doubtful as to whether or not a gas turbine emits less CO2 than a diesel engine, I can't see anything authoritative, but I can see sources that suggest about 250 to 300gCO2eq/kWh for diesel vs 400 to 500gCO2eq/kWh for Gas turbines. You probably get fewer other pollutants (NOx and other particulates) out of a gas turbine.