Signing files individually will create independent signatures for the contents (not filename) of each file. A potential downfall here is that the items could be removed or renamed without detection.
Let's say, for example, the files to be signed are alice-invoice, bob-invoice, and chris-invoice. If each file is individually signed, and bob-invoice is deleted, there is no way to detect the deletion.
Creating a list of files and hashes protects the integrity of the entire set of files because and allows the detection of file deletion or renaming. A potential downfall here is that proving the validity of a single file (to a third party) requires divulging the entire list of filenames and hashes.
In this case, if we need to prove that alice-invoice hasn't been modified, we must reveal the entire list (to prove the signature is valid), which reveals that we have invoices for Bob and Charles.
Another consideration: strictly speaking, the question only compares two uses of clear signatures. A clear signature includes a complete copy of the original file. That means that signatures of individual files must be protected with the same level of security as the original files. (This is another potential downfall of that method.) Detached signatures are smaller and do not reveal the contents of the signed file and may be worth considering.