<p>As per <a href="https://stackoverflow.com/questions/41970/lightweight-fuzzy-search-library#41975">this</a> comment in a related thread, I'd like to know why Levenshtein distance based methods are better than Soundex.</p>

Soundex is rather primitive - it was originally developed to be hand calculated. It results in a key that can be compared.
Soundex works well with western names, as it was originally developed for US census data. It's intended for phonetic comparison.
Levenshtein distance looks at two values and produces a value based on their similarity. It's looking for missing or substituted letters.
Basically Soundex is better for finding that "Schmidt" and "Smith" might be the same surname.
Levenshtein distance is better for spotting that the user has mistyped "Levnshtein" ;-)