For the problem I\'m working on, finding distances between two sequences to determine their similarity, sequence order is very important. However, the sequences that I have are
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.