Hi, welcome
There's a replay option built into Civ4. However, I think you need to have a copy of the Replay file that was generated when the game finished. You also need to have the same mod loaded if the original game was played using a mod. This is primarily designed as a way to see a replay of your own games. Note that there is no way to see action replays of specific battles. You just get to see key events that occurred during the game.
Here's one alternative that may interest you.
I am involved in running the Game of the Month (GOTM) series of competitions, where multiple players all start with the same map and scenario settings and play the game to try to achieve the maximum scores or fastest victories. We now have over 6,000 submitted saves for Civ4 Vanilla alone, and a total of around 10,000 if you include Warlords and Beyond the Sword. We also run a Succession Game competition called SGOTM, and over 160 teams have played in 10 games. These competitions are also run for Civ3. We have our own
web site supporting them.
The results of all these competitions can be found
here and
here (SGOTM), and you can run replays of the submitted games by selecting the game and player of interest
here. The Replay facility doesn't work with Internet Explorer, but any other modern browser will do. You can use it to replay two players' attempts in parallel to compare their progress.
Many of the leading players in these competitions also post "spoilers" describing the way they approached the games. You'll find these in the
Civ4 Game of the Month forum, and this is where we announce new games every month. The Civ4 and Warlords competitions support both Mac and Windows players, and we hope to extend the Beyond the Sword competitions to Mac players as well.
Hope this helps.