Benefits of applying decomposition strategies in large-scale process mining projects:

1. Efficiency: Decomposing a large process into smaller parts enables the process mining tool to operate faster and more efficiently. It uses fewer resources and provides results quicker. 

2. Scalability: Decomposition strategies allow for the analysis of very large event logs that would not be feasible to process as a whole. 

3. Readability: Large process maps can become complex and difficult to understand. By breaking down these processes, the resulting maps are often simpler and easier to read.

4. Accuracy: By decomposing a process, certain sections can be analyzed in greater detail, leading to more accurate and detailed insights. 

5. Flexibility: Decomposition allows for parallel processing and distributed computing, enabling flexible and efficient use of computational resources.

Challenges of applying decomposition strategies in large-scale process mining projects:

1. Loss of Context: Decomposition can transform complex processes into simpler ones. However, there is a risk of losing the context or ignoring dependencies between different parts of the process. 

2. Increased Complexity: While decomposition can simplify the representation of individual processes, it can introduce additional complexity in terms of how these processes interact and coordinate with each other. 

3. Errors in Decomposition: Incorrectly decomposing a process can lead to inaccurate or misleading outcomes. This makes the decomposition step crucial and can require considerable expertise.

4. Overhead: Decomposition involves additional steps in the process mining project. This can add more overhead in terms of time and effort for setting up, as well as additional computations.

5. Requirement of Expertise: Effective decomposition strategies often require a high level of understanding and knowledge about the process and the underlying business. This could be a constraint in environments where such expertise is scarce.