1. Data Processing Mechanism: Hadoop is a distributed data processing framework that enables large-scale data processing using a cluster of computers. It utilizes a distributed file system called Hadoop Distributed File System (HDFS) and a processing framework called MapReduce. On the other hand, Lucene is a full-text search library that provides indexing and searching capabilities to retrieve information from unstructured or semi-structured data.

2. Data Storage: Hadoop stores data in a distributed manner across a cluster of computers, allowing high availability and fault tolerance. It breaks down large files into smaller blocks and replicates them across different nodes. In contrast, Lucene does not store data in a distributed manner. It uses its index structure to store and retrieve data efficiently within a single machine.

3. Scalability: Hadoop is highly scalable and can handle large volumes of data by simply adding more nodes to the cluster. It can scale horizontally by adding more commodity hardware, achieving high throughput and processing power. Lucene, on the other hand, is not designed to scale horizontally like Hadoop. It is more suitable for smaller datasets and can run on a single machine or a small cluster of machines.

4. Data Processing Paradigm: Hadoop follows the MapReduce paradigm, which involves dividing the data into smaller chunks and processing them in parallel across different nodes. It is well-suited for batch processing and analyzing large datasets. In contrast, Lucene employs an inverted index mechanism to enable efficient searching and retrieval of information. It is optimized for real-time search and indexing, making it ideal for applications that require quick search capabilities.

5. Data Accessibility: Hadoop provides a distributed file system (HDFS) that allows data to be accessed and processed by multiple concurrent tasks or applications. It provides a shared storage space for various data processing jobs. On the other hand, Lucene indexes data within its own structured file format, making it accessible only to the application using the Lucene library.

6. Use Cases: Hadoop is commonly used for big data processing, including tasks like log analysis, data warehousing, and large-scale data analytics. It is suitable for scenarios where handling large volumes of data is essential. Lucene, on the other hand, is primarily used for text search and information retrieval. It is widely used in applications like web search engines, document search, and recommendation systems.

In Summary, Hadoop is a distributed data processing framework designed for handling large-scale data processing and analytics, while Lucene is a full-text search library optimized for efficient searching and retrieval of information from unstructured or semi-structured data.