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Freeze dried food is...well...dry, and should to be kept that way until you are ready to eat it.

For short-term storage, for example food that will be eaten within a few days, the easiest way is to place the food in a zip-lock style baggie and squeeze as much air out of the baggie before zipping it closed.
This will help remove as much air, and just as importantly moisture, from the bag.

For medium-term storage you may store freeze dried food in a vacuum. For this purpose you may use a Seal-a-Meal type vacuum sealer.

For long-term storage we recommend that you place your freeze dried food in a mylar bag with an oxygen absorber and heat-seal the bag properly.

There is a significant amount of documentation stating the benefits of freeze drying vs dehydrating food.

Most of the research that we have found indicates that while freeze drying may remove up to 5% of the nutrients found in fresh food dehydrating removes between 40%-50% of the nutrients found in fresh food.

The significant loss of nutrients lost in the dehydrating process is due to the high temperatures usually used by home and commercial dehydrators.

For most foods, and for most people, the answer is simply yes.

That being said, many people will find that while the food "tastes the same" as it did prior to the freeze drying process the freeze dried food often times seems to "enhance" the flavor.

An example of this are Mint Chocolate Chip ice cream sandwiches. (Which are very good by the way)
The freeze drying process seems to enhance the mint flavor of the sandwich.

Another example of this are raw strawberries.
These tend to come out "bright" or "stronger" in strawberry flavor.