Based on the definitions in my first "real" dictionary (New World Dictionary of the American Language, Second College Edition, 1980), I've always understood zeugma to be the clever one and syllepsis to be the boring one.
zeugma: a figure of speech in which a single word, usually a verb or
adjective, is syntactically related to two or more words, with only
one of which it seems logically connected (Ex: The room was not light,
but his fingers were)
syllepsis: a grammatical construction in which a single word is used to modify or govern syntactically two or more words in the same
sentence, though it can grammatically agree with only one of them
(Ex.: either they or I am wrong)
Actually, I find I have a cavil with the above definition of zeugma: although it contrasts "logically connected" with an implied "illogically connected," the example illustrates "concrete" vs. "figurative."
Anyway, the point is that, according to these two definitions, syllepsis represents a grammatical strain; zeugma is more of a semantical mixture.
Now, from another "real" dictionary (The Compact Edition of the Oxford English Dictionary, Complete Text Reproduced Micrographically, 1971):
zeugma: A figure by which a single word is made to refer to two or more words in the sentence; esp. when properly applying in sense to
only one of them, or applying to them in different senses; but
formerly more widely, including, e.g., the use of the same predicate,
without repetition, with two or more subjects; also sometimes applied
to cases of irregular construction, in which the single word agrees
grammatically with only one of the other words to which it refers (more properly called Syllepsis).
syllepsis: A figure by which a word, or a particular form or inflexion of a word, is made to refer to two or more other words in
the same sentence, while properly applying to or agreeing with only
one of them (e.g. a masc. adj. qualifying two sbs., masc. and fem.; a
sing. verb serving as predicate to two subjects, sing. and pl.), or
applying to them in different senses (e.g., literal and metaphorical).
Here, the overlap between the two words is brought out a bit more; however, the distinction can still be seen: zeugma causes a word to serve double (or more) duty in terms of sense; syllepsis does so in terms of syntax.