Negligible my foot. If it was negligible why do large cargo ships all use diesels instead of turbines? Or trains for that matter.
Different use case , most destroyers , cruisers use turbine.
If you care about acceleration, and maintaining a high speed you would use turbine, in this case tanks do need it.
As you said , cargo ships and trains doesn't , for the exactly the reason they don't require high acceleration , only economy.
Different kind of work loads can drastically change the fuel consumption even with the exact same engine , you can try that with your own car, step on the gas paddle for the yellow light for a month , and waiting for the next light for a month , you will see a noticeable difference in the fuel economy.
It makes sense that for the work loads that is typical for a tank , diesel and turbine in these days are very similar.