Luminescence, fluorescence and absorbance are the three most common methods used in these assays. In general, luminescent assays are more sensitive than fluorescent assays, and fluorescent assays are more sensitive than absorbance assays. Whatever the assay method, detecting low level or small changes in a target requires a sensitive assay. For example, when studying an enzymatic reaction, you don't want to have to add a high level of substrate enzyme or catalyst to drive the reaction to a detectable level because this creates an artificial system that does not reflect physiological conditions. Instead you want your assay to be sensitive enough to be performed at near physiological levels, thus generating more biologically relevant data.
High sensitivity lets you detect samples that less sensitive methods might miss. But what happens when you have a plate of experimental samples with varying signal strength? How can you be sure that the assay signal from one well is not partially the result of a strong signal from the adjacent well? In plate readers, this is defined as well-to-well crosstalk.