As per MS normal azcopy depends on the CPU but blob to blob is serverto server APIs so as use AZCOPY_CONCURRENCY_VALUE= more than 1000.

https://learn.microsoft.com/en-us/azure/storage/common/storage-use-azcopy-optimize?toc=%2Fazure%2Fstorage%2Fblobs%2Ftoc.json#increase-the-number-of-concurrent-requests

” If you’re copying blobs between storage accounts, consider setting the value of the AZCOPY_CONCURRENCY_VALUE environment variable to a value greater than 1000. You can set this variable high because AzCopy uses server-to-server APIs, so data is copied directly between storage servers and does not use your machine’s processing power. ” 

Previously it was taken more than 30 mins to download the data but once we provided AZCOPY_CONCURRENCY_VALUE=2000 and was able to copy from blob to blob in 3.41 minutes.