Answer:
In the first story, Holmes prevents a crime from occurring; in the second story, Holmes resolves a case in which a crime had already occurred.
The person guilty of committing a crime is arrested in "The Red-Headed League," but in "The Adventure of the Blue Carbuncle," the criminal remains free.
Step-by-step explanation:
In first story, a bank robbery is planned that is prevented. In second, a robbery of gemstone "Blue Carbuncle" had already taken place and the robbers had to be caught.
Both cases were solved by Holmes and Watson on their own. In first story, they needed police ot catch th criminal. In 2nd story, they let the criminal go because handing him would have made him a more hardened criminal. So in 2nd story the criminal remians free.
In both story they had clues and had no difficulty in looking for evidences and clues.