Because I can never remember, and the Technet documentation is not helpful in this regard:
/Check - Calculate Checksums (Check.Checksum. Got it!)
/Verify - Just compares source and destination.
The /verify option works as you might imagine: It double-checks that either a capture or apply operation didn't accidentally drop any bits along the way. WIM files are pretty large, and although network and disk read/write operations already contain built-in checks, just one misplaced byte can render the image or system useless. The /verify option helps prevent that from happening. After either applying or capturing a windows image, ImageX compares the source data and its copy, searching for (and correcting) differences. ImageX enables the /verify option by default whenever applying or capturing over a network connection, but it doesn't do that when working with local external storage, so it's never a bad idea to add the /verify option. (It will, of course, slow things down a bit.)
The /check option has a similar purpose but a slightly different and perhaps more efficient approach. If you include /check when capturing an image, ImageX creates a hash of every 10MB chunk of ImageX data, then embeds those hashes in the resulting WIM. Including /check on an apply operation causes ImageX to check the applied image by re-computing hashes on that image, then comparing those computed hashes with the embedded ones. Thus, /check certifies not only that a WIM wasn't mis-copied during the apply operation but also that a WIM hasn't become corrupted while stored. Why use /verify, then? Why not just always use /check? The answer is that /check can't do its job on an apply operation if no one specified /check on the capture. If the WIM lacks embedded hashes, /check can't check the hashes. The /verify option, in contrast, doesn't need hashes, so it can always help.