Firtz is great for recommending moves and analysing games and positions. The engine moves pieces on the board. It's also good for searching for games from megadatabases of master's games.
Chessbase is great for searching games and arranging games and positions into databases, and keeping an number of boards and databases active at the same time. It makes a great analysis board while playing correspondense chess. You can also generate win/loss statistics and opening books and trees from any database, which I don't think you can do in Fritz. When you want it, the engine can make recommendations via arrows on the board, algebraic notiation output of engine calculatons for next move (kabitzer), etc., but the engine doesn't actually move pieces. You can turn all the hints and kabitzers off when you don't want them and they stay off. I keep them always off and go to Fritz if I want move recommendations.
The problem with Fritz as an analysis boad for correspondense chess is that the engine turns back on every time you load a new game or position or make significant modifications to the pgn in a game. You have to keep turning it back off. Ocassionally it's gonna make a move when you didn't want it to and give you a hint.
If you can only buy one then probably Fritz. An older version is fine. I have Fritz 9 and like it.
If you can buy both, then I'd also recommend Chessbase 9 starter package.
I have been looking to improve my chess game using a computer program, but I don't know if I should go with Fritz or Chessbase. Are they similar? Do they have differences? Does Fritz use Chessbase as it's database?