I am having glass block windows installed in our basement. My question is the differences between using mortar vs. using silicone to install the windows. The contractor I am using is planning on using silicone but I do not really know which method is better. Thanks for any help.

Follow the recommendations of the glass block manufacturer. My GUESS is that they will recommend mortar.

For more security the cement works much better.
But like Richard said. Check with the manufacture of the block.
Also the size of the opening being enclosed also has a factor on which to use. With small basement windows silicon will work fine.

How does silicone hold up to the weather elemnts (snow, rain) compared to cement? Will the silicone have to be reapplied on a regular basis?

You must use the material suggested by the block manufacturer. There are diffrent types of silicone all for diffrent types of uses.
Generally Silicone will last a long time.
Your not using this stuff like cement. Its only a very small thin amount between the blocks to be used as a glue, Your not building this up to a thickness like cement. Very little of the stuff will be exposed to the weather so it will last a very long time. As long as you have the stuff suggested by the manufacture of the block.
If you use the wrong stuff it can break down because of sunlite exposure.

I think you can use both, just leave a gap for the silicon. Is it something like this ? glass build in wall