Freedoom's textures are not ordered the same as Doom's.
To demonstrate this, run Doom and save the game. Quit and restart the game exactly the same but with freedoom.wad loaded. Reload the game and all of the textures will be changed.
This is a fairly unimportant example, but it has other potentially more serious implications. Some multiplayer ports (eg. Odamex or ZDaemon) may use the texture number in their network communications. In this situation, there may be compatibility problems when mixing Doom and Freedoom clients and servers.