XACT is a high-level API for audio playback. XACT is implemented in terms of differing lower-level APIs on various platforms, some of which are actually deprecated. DirectSound, for example, is used to implement XACT on older version of Windows and DirectSound itself is deprecated.
On the 360, XACT is implemented in terms of the Xaudio stack; it's thus technically a cross-platform API, although not in the same fashion (as in, not supported by as many platforms as) something like fmod.
You can use XACT via XNA on the 360, and in fact that remains the last current SDK of any type (as of this writing) to support the API -- it's use is no longer supported on Windows as of Windows 8 (June 2010 was the final release of the DirectX SDK, the components formerly provided by that SDK have been integrated into the Windows SDK itself, and the latest version of that SDK removes support for XACT on Windows).
In the sense that XACT and DirectMusic were both built on DirectSound (and are now both deprecated on Windows), they are analogous. However, XACT only ran through DirectSound on XP -- on Vista and 7, it ran through the OS's rebuilt audio stack, primarily the Audio Session API.