I was just wondering what's the difference between these two detergents in cell lysis buffer. And I am planning to use the cell lysate to do the GFP-trapped pull-down assay.
There is no major difference between the performance of these two detergents. Both are non-ionic and both can be used for pull-down experiments. Sometimes the interaction is dependent on the detergent used so testing different detergents could help. Also, take into consideration where your protein is located within the cell as non-ionic detergents tend to extract only cytoplasmic proteins.
Digitonin is a steroid detergent used to selectively permeabilise the (cholesterol-containing) plasma membrane. Given its high price and its toxicity, it is used only where needed. Triton X100 is a general purpose, non-ionic detergent that is used to solubilise membranes, prevent protein-protein interactions and "sticking" of proteins to vessel walls by hydrophobic interactions. In pull-down, it can prevent unspecific interactions and thereby give cleaner results. Often, other detergents with different properties are added for this purpose, this could include ionic detergents like SDS or steroid detergents.