That is a really good question, and the answer depends entirely on your situation and your point of view. There is a good case to be made for each. What may be helpful is to understand the reason each has its supporters before discussing the choice with a CSIA certified chimney sweep.
Top of the Line
Top down dampers, or top mount dampers, are relatively new to the world of chimneys and, as their name suggests, are mounted at their tops. When the fireplace is not in use, they can be closed to function as temporary chimney caps. That is to say, when a top damper is closed, the chimney is shut at the top to rain, snow, debris, and animals.
Obviously, that cannot be the case when there is a smoke-producing fire or its smoldering embers under a top-down damper. When that is half the night and half the year, the “chimney cap” comparison falls apart to a considerable extent. The other argument for top dampers remains, however, in that the length of the chimney stays warmer when it is closed at the top.
Stuck In Throats
Throat dampers are the traditional kind and are actually part of the fireplace as opposed to the chimney. They close off the chimney at its bottom, which means the top definitely needs a cap to keep everything out of the chimney. Throat dampers keep the house warmer by shutting out the cold air in the chimney.
Because of their location, they are very difficult to replace, so usually a top damper is recommended when a throat damper is no longer working. At that point, the top-down choice becomes more economical. It may also reduce the rate of creosote condensation, given a warmer chimney. This is the kind of thing that needs to be discussed with a certified sweep looking at the fireplace system in your house.