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External hard drives typically offer the highest storage capacity among the options listed. These devices are designed for substantial data storage and can hold anywhere from a few hundred gigabytes to several terabytes of data, making them suitable for backing up entire systems, storing large media files, and accommodating extensive collections of documents and applications.

In contrast, while Blu-ray discs provide considerable storage—usually around 25 GB for single-layer and 50 GB for dual-layer—they are still limited when compared to the capacity offered by external hard drives. Flash drives, although convenient and portable, also have more restrictive storage capacities, often ranging from a few gigabytes to several terabytes, but they don't generally reach the highest levels that external hard drives do. Standard CDs are much smaller in capacity, typically holding just 700 MB, which is significantly less than what external hard drives can offer. Hence, the external hard drive stands out as the storage device with the most capacity available, making it the best choice in this context.