Choosing between the two fans is dependent on the task or project at hand. Considerations include the size of the space you need to cool. If you have a larger space, a centrifugal fan may be a better choice, as its output pressure is greater and can force air to circulate at a greater distance. However, if the space needing to be cooled is smaller, then an axial fan may be a better choice, as the airflow does not need as much pressure behind it to force the air at a further distance.
Another point to consider is the size of the fan you need. Whilst both fan types come in varying sizes, the axial fan produces a lot more noise and so a centrifugal fan may be the better choice. However, axial fans are usually lighter units compared to centrifugal fans.
An axial may be a wiser choice if you are housing a unit in a weaker infrastructure, or in machinery that needs to be movable. Even more so, if the power supply is weak, then an axial fan may be more appropriate due to its low-pressure output. A centrifugal fan requires more input of power for a high-pressure airflow.
Finally, another attribute that needs to be considered is budget. If you have a limited budget to work with, then axial fans are the most cost-effective solution. They are as reliable as centrifugal fans, but their lighter weight and lower energy needs mean that they are cheaper to purchase and maintain.