In the depths of winter, not having to venture outside to an office will be a winner.
An extension to the house will likely cost a little more to build, but done right it will also add more value to the house. If can be tied into the main heating system, saving on heating costs, and can adapt as your needs change.
Future buyers not looking for an office might like a playroom or extra bedroom or living room, and those who do want an office might value being close to the kitchen or a bathroom or being in the house when there are kids about. An office built in a garage will only really have value to people who want a separate office.