As Greg mentioned Palm Springs is walking distance to downtown which is it's big plus. I believe it's a motel conversion (it sure looks like it even if it's not) and is a much smaller resort than Indio. The downside is that the last time I was there it was in need of a remodel (especially the common area, lobby carpeting, etc), the rooms were fine. The other downside is that I'm really sensitive to road noise and if you get a unit facing the street which is most of the 1 bd and some of the 2 bd it can be really noisy. When I go there in the future I will only reserve a studio because they are guaranteed to be in the courtyard by the pool.
We prefer Indio unless we are going in the dead of winter. The pools, etc are much better. The resort is at the end of residential area, next to a golf course so much quieter. The grounds are very well landscaped. The first hour at the lazy river floats are not allowed only walking, good exercise. The main pool is definitely noisier than the Palm Springs pool, but there is a secondary pool which is usually quiet and is about the same size as the Palm Springs pool. We usually ask for a room away from the main pool (I can only take so much of Marco Polo) and have had good luck getting them.
If I'm booking in the dead of winter I'd pick Palm Springs but any other time of the year I pick Indio.
Can't speak for Cathedral City, never been there.
Ian