Technically the 4 inch pads are a standard thickness (industry standard is between 1 inch and 1 1/2 inches thick). Low profile pads are generally considered any thing less than 1 inch thick.
The reason they feel different or may be harder to control is because the aspect ratio is off. On a 1 1/2 inch thick, 4 inch diameter pad you will have the feel of an 8 inch pad that was 3 inches thick.
The flip-side is that smaller diameter pads are less forgiving of changes in angle relative to the paint. Since there is less foam (over-all) to compress, just the weight of the machine can compress the small pad enough that interference becomes an issue. It becomes very easy to run the backing plate into the paint.