The most common and most likely answer to this crossword clue is the 3 plus 4 plus 12 letter word MAD DOGS (ENGLISHMEN)
I've seen this crossword clue in The Guardian
M
A
D
D
O
G
S
(
E
N
G
L
I
S
H
M
E
N
)
Buddy explains!
The straight part
We know that "Their bite’s worse than their bark" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case their bite’s worse than their bark = mad dogs (englishmen).The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.