How are they different?
They were look similar (Activated alumina and molecular sieve, they both come in a small spherical beaded shape), they perform the same process (AA and MS adsorbed material at a molecular level), and they both have regenerative properties (you can re-use the material once the desiccants has reached capacity), yet they are two completely different products. So the question is, with so many similarities, how are they different?
What they are made of is a good starting point. Activated alumina is made out of aluminum oxide that is highly porous, while molecular sieve is made out crystalline metal aluminum-silicates. What this means is the pores on molecular sieve can be shaped into specific sizes most commonly seen as 3A, 4A, 5A, and 13X, where as activated alumina's pores do not have specifically measured sizes. This means molecular sieve can be used to separate certain molecules of specific sizes from one another, for example removing ammonia from natural gas streams.
From an application standpoint, here is how they differ. Activated alumina has a real strong water adsorption capacity, it can adsorb a lot more water than molecular sieve, this makes it a very useful material in air compressors or for certain natural gas processing applications. The durability of the material allows it withstand a lot of pressure along with high levels of humidity.
Activated alumina can't adsorb the large variety of materials or separate certain molecules from one another like molecular sieves can, making it ineffective in a process like ethanol dehydration. This is because activated alumina would be able to adsorb both ethanol and water molecules and thus no separation would occur.
Molecular sieve may not be able to adsorb as much water but if you needed to reduce water to very low amount, up to 0.1ppm, molecular sieve would be your absorbent of choice because this is something other adsorbents besides molecular sieve have been incapable of doing.
Molecular sieve can also be used to separate specific molecules from one another, due to the customization of their pore sizes. For example you can separate water from ethanol, and carbon dioxide, ammonia, and larger hydrocarbons from natural gas streams, which is something activated alumina can't do, or won't do with same efficiency.