The following quotation from George Puttenham, "The Arte of English Poesie" (1589) appears in William Rushton, Shakespeare and 'The Arte of English Poesie' (1909):
There is a decency in respect of the persons with whom we do negotiate, as with the great personages, his egals to be solemn and surly, with meaner men pleasant and popular, stout with the sturdy and mild with the meek, which is a most decent conversation and not reproachful or unseemly, as the proverb goeth, by those that use the contrary, a Lion among Sheep and a Sheep among Lions. Right so in negotiating with Princes we ought to seek their favour by humility and not by sternness, nor to traffick with the by way of indent or condition, but frankly and by manner of submission to their wills, for Princes may be lead but not driven, nor they are to be vanquished by allegation, but must be suffered to have the victory and be relented unto.
It thus appears that "to be a lion among sheep and a sheep among lions" was, in the late 1500s, a proverbial way to refer to someone who was bold and decisive (or arrogant and overbearing) among his perceived inferiors but meek and deferential among his superiors. That type of person is surely as familiar to anyone who has worked in a hierarchical organization today as it was to George Puttenham in 1589.
The poster's friend, seems to have a different meaning in mind—namely that it is better be to be a powerful figure among weaklings than a weak figure among the powerful. Nevertheless, there may be some echo of the older proverb in the friend's assertion; certainly the formulation is strikingly similar.
Morris Tilley, A Dictionary of the Proverbs in England in the Sixteenth and Seventeenth Centuries (1950) cites Pullenham's use of the expression and links it to another proverb about circumstantial boldness: "who takes a lion absent fears a mouse present." Yet another old proverbial expression that Tilley cites is "as fierce as a lion of Cotswold"—an expression that goes back to 1530 and whose original meaning seems to have been "one who pretends to be fierce when surrounded by sheep" (there being no actual lions but lots of actual sheep in Cotswold); eventually the figurative meaning of this phrase came to be "a sheep"—evidence that a lion that tarries among sheep may become a sheep himself, if indeed he was not one all along.