What are the main differences between the Knuth-Morris-Pratt and Boyer-Moore search algorithms?

In an rough explanation

Boyer-Moore's approach is to try to match the last character of the pattern instead of the first one with the assumption that if there's not match at the end no need to try to match at the beginning. This allows for "big jumps" therefore BM works better when the pattern and the text you are searching resemble "natural text" (i.e. English)

Knuth-Morris-Pratt searches for occurrences of a "word" W within a main "text string" S by employing the observation that when a mismatch occurs, the word itself embodies sufficient information to determine where the next match could begin, thus bypassing re-examination of previously matched characters. (Source: Wiki)

This means KMP is better suited for small sets like DNA (ACTG)

Moore's UTexas webpage walks through both algorithms in a step-by-step fashion (he also provides various technical sources):

• Knuth-Morris-Pratt
• Boyer-Moore

According to the man himself,

The classic Boyer-Moore algorithm suffers from the phenomenon that it tends not to work so efficiently on small alphabets like DNA. The skip distance tends to stop growing with the pattern length because substrings re-occur frequently. By remembering more of what has already been matched, one can get larger skips through the text. One can even arrange ``perfect memory'' and thus look at each character at most once, whereas the Boyer-Moore algorithm, while linear, may inspect a character from the text multiple times. This idea of remembering more has been explored in the literature by others. It suffers from the need for very large tables or state machines.

However, there have been some modifications of BM that have made small-alphabet searching viable.