Windows copy will work but will take a long time to copy large libraries completely. Backup software will backup only new or changed files which is faster. I have Seagate drives that each comes with reliable backup software pre-installed that I would recommend.
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I'll second Mapman's comments. Regarding file copies being bit-perfect, hard drives are very reliable in terms of data integrity these days, and employ sophisticated error detection and correction algorithms to detect errors, and correct them bit perfectly. If undetected and uncorrected errors occurred with any regularity, word documents, financial spreadsheets, jpg pictures, and all kinds of other files would get messed up at times as a result of being copied within a drive or between drives.
But if you want to go to the trouble of verifying that, you can use a program which computes file "checksums," and compare the checksum of the original file and the copy. Some programs which do that are listed here.
Also, the following statement from this Wikipedia writeup is of interest:
Only a tiny fraction of the detected errors ends up as not correctable. For example, specification for an enterprise SAS disk (a model from 2013) estimates this fraction to be one uncorrected error in every 10^16 bits [ten raised to the 16th power], and another SAS enterprise disk from 2013 specifies similar error rates. Another modern (as of 2013) enterprise SATA disk specifies an error rate of less than 10 non-recoverable read errors in every 10^16 bits. An enterprise disk with a Fibre Channel interface, which uses 520 byte sectors to support the Data Integrity Field standard to combat data corruption, specifies similar error rates in 2005.Roughly speaking, 10^16 bits is around 1,000 terabytes(!). And presumably most of that tiny handful of uncorrected errors which may occur in copying 1,000 terabytes (far more data than most of us are likely to copy in our lifetime) would be detected, and an error indication provided to the user.