Inflatable mats are much comfier than foam mats and offer better insulation against cold. However they are heavier, more expensive and are vulnerable to punctures, not all of which are easily mended. On a long expedition it is wise to take a foam mat as well, and we would not recommend an inflatable mat for alpine type bivis where they may be easily damaged.
Thermarest invented the modern inflatable mat, and in our opinion, with the possible exception of Exped, their products are the best available. What could be better than a Thermarest? Well for Arctic and similar use, an Exped Down-Filled Air Mattress. This is a relatively new innovative concept that we can personally vouch for as superb. Voted European Outdoor Award Product of the Year 2002/3.
All these mats come with a stuff sack. However, it is best to store inflatable mats unrolled, and with the valve open so as to prevent condensation forming internally.