The magnetic filed typically produced by rare-earth magnets ( neodymium magnet) can exceed 1.4 Teslas, whereas ferrite or ceramic magnets typically exhibit fields of 0.5 to 1 tesla.  So Neodymium magnet is stronger than ferrite & ceramic magnet. 

The pull force of same size of ferrite magnet is around 1/7th of neodymium magnet pull force.

Neodymium magnet breaks easily which ferrite is much more resistant and resists breakage. Both magnets retain their magnetic force over time , and there is no reason to fear losing the magnetism naturally. However, ferrite magnets can be demagnetized by the influence of stronger neodymium magnets. 

Neodymium magnet need third processing ( Wire cutting or drill hole) after pressing while ferrite magnet only need pressing. 

For small qty or samples, you can get faster delivery for neodymium magnet while you need longer time for ferrite magnet if you didn’t have existing mould.

Another important difference between neodymium magnet and ferrite magnet is their material cost. Neodymium magnet raw material is about 100 times of ferrite magnet’s. When your design your products and its magnet, you have to put the cost into consideration if it is big quantity.