You have to be running the latest drivers from creative for your Audigy. The problem is stated very clearly in the release notes.
3.2 Sound issues
If using a 3D sound accelerator such as the Sound Blaster Audigy series sound card, you can go into "Options/Audio" to enable EAX 3.0 by selecting the "Hardware 3D Sound + EAX" options.
You need to upgrade to the latest version of Sound Blaster Audigy drivers in order to get acceptable 3D sound performance.
Using Unreal Tournament 2003 in conjunction with earlier versions of the drivers MAY cause severe performance problems (major slowdowns in the order of 30-50% while playing sound) in which case you should change the option back to the default "Software 3D Audio".