Im not entirely sure what youre refering to, but Im pretty sure there are actually 2 versions floating around.

One of them starts off right in the first area (the town), has a higher-res hud, and a glitchy dungeon-basement-flooded area-thing. EXE file is Jazz3.exe with the Unreal Icon dated 11/16/1999. Also worthy of note there was a Documentation folder containing progress notes (which so happen to state the glitchyness of the dungeon). I suppose this document would be legal to distribute if anyone cares to see? This version has more files in the Textures folder.

The other starts off with Jazz on treadmill like object, a "Welcome to Jazz Jackrabbit 3D" voice and menu music, a more pixilated HUD, and nicely done dungeon-basement area. EXE file is Jazz3d.exe with a JJ3 icon and dated 10/6/2000. It seems this version has all superiority aside the lower-res HUD (which I dont know where it is stored to be able to replace it with the high-res one). This version also has more files in the Maps folder.
EDIT: Oh yes, and the crosshair doesnt seem to change in this one

I also vaguely remember (Ill have to check) the 2 versions have different firing rates of the blaster
EDIT2: Just checked, the version mentioned first has a faster blaster