First, I'd want to know how they determined your gears were OK. Did they take photos? If so, I'd want to see them. Any surface degradation on bevel gears will make them noisy.
Second, synthetic gear oil is gear oil. Unless it's olive oil, it's OK to use. The second number (140 in your case) is the viscosity at operating temperature. You should see a temperature rise comparing 90 weight and 140 weight oil, but that's not the whole story. Although thicker oil runs hotter due to increased friction, it also insulates metal better than thinner oil. The difference in operation depends on external cooling capacity and oil volume. This is hard to assess in the case of an axle, unless you've got experience with the specific design.
FWIW, when I built 4WD axles for industrial/farm use, the specification was for either 90 or 140 weight. The difference came down to ambient temperature more than anything else. Corn field tractors run hotter than rice paddy tractors. Same axles.