I still own a 1DmkII, and my understanding of its AF is from that experience, not with the 1Ds.
The early 1D models, 1D, 1DII, 1DIIn, !Ds, 1DsII, all used a similar 45 point AF sensor as was developed for the previous film body, 1Dv. The software varied slightly with model, but this was a pretty well developed sensor with all of the points being applied in the AI mode to track moving subjects. At least moving subjects was the priority of the 1D bodies, but the corresponding 1Ds bodies were always announced many months after the corresponding 1D bodies, and had a bit more development time.
The physical AF sensor was the same, but the 1.3X crop of the 1D series made the spread of the AF points fill a much larger proportion of the image frame. Depending upon your use, this may be a significant difference to you. The 45 AF points in the 1Ds is effectively a much smaller cluster in the frame center as opposed to the 1DII. Note that the 1D bodies also used identical FF lenses, so the incident angle of light from opposite sides of the lens had exactly the same sensitivity to phase differences as in the 1Ds bodies.