Hamming Distance vs. Levenshtein Distance

That question really depends on the types of sequences you are matching, and what result you want.

If it's not a problem that "1234567890" and "0123456789" are considered totally different, indeed Hamming distance is fine.

In addition to the right Johan answer, the padding can be problematic.

For example, when you compare 123 to 123456 it's different if you pad either at the end of the string or at the start of the string. The similarity of ___123 with 123456 is 0, but The similarity of 123___ with 123456 is 3.