That's difficult to answer, but generally, acidic spills present the most challenges, primarily because carpeting is receptive to acid-based colorants. Specifically, coffee can be difficult because it is generally hot, and the heat acts as a catalyst for dye reaction. Another difficult stain is urine, which also goes on at an elevated temperature. Urine starts out acidic, and forms salts which aren't soluble in water, so cannot be readily rinsed out. To further complicate things, urine then breaks down into other reactive chemicals, and becomes very alkaline. So, the acid in urine sets the yellow stain, and then alkalinity further damages and bleaches the carpet fiber. Meantime, the urine has seeped into the carpet backing, padding, and sometimes even the sub-floor, creating odor problems that can be tough to fix. Other tough spills include ink, orange juice, tomato sauce, tea, mustard, and the like.
Here's a tip for your red wine spill: Blot up what you can, then use white wine to rinse it out! In the chemistry of carpet stain removal, the first rule is "like displaces like". That's why our simple homemade spot removal formula has acidic vinegar in it - and by the way - it's a better choice than the white wine.