And on the other leg

BBC America's Anglophenia blog chips in with a charming entry on the phrase:
It’s a description of someone who is boorish and loud, and a little too full of his or herself. It’s analogous to expressions like “cock of the walk” or (going a little further back) “popinjay” or “coxcomb.” The point is not that this is a person who definitely can’t fulfil his or her promises; it’s that this is someone who is boastful about being the most attractive, most astonishing person in the room: a windbag, in other words.

Blog author Fraser McAlpine then goes on to discuss the 'no trousers' variant, to which he gives equivalent consideration as 'a more definite expression'. While arguably correct in terms of common usage, it really should be noted that this is a late bastardisation rooted in the London media scene of the 1980s, without the elegance or sense of the original.

The one should not be considered as a stronger version of the other, as it's extremely unlikely that both would be used by the same speaker. Adherents to the bastardised version, as has been noted, tend to typify the meaning of the original.