The biggest cause of fatality on Kilimanjaro is altitude sickness. Therefore, the safest route will be the one which allows for the best acclimatization.
Grand Traverse on Kilimanjaro is one of the longest routes. It offers plenty of opportunities to climb high and sleep low. This is the best way to get your body used to the high altitude and reduce the severity of altitude sickness. Furthermore, it also ascends very gradually over multiple days. Therefore, it also has some of the highest summit success rates.
Besides acclimatization, the Grand Traverse avoids the dangerous Western Breach as well as the Barranco Wall. Therefore, the Grand Traverse could be deemed the safest route together with the Northern Circuit and the Rongai Route.