First of all, despite the movies portrayal of this, the canon (J.K. Rowling's books) indicated that both schools were, indeed, technically co-ed:
Harry, whose attention had been focused completely upon Madame Maxime, now noticed that about a dozen boys and girls, all, by the look of them, in their late teens, had emerged from the carriage and were now standing behind Madame Maxime.
The Durmstrang students were staring curiously at Harry too. Out of the corner of his eye, Harry saw comprehension dawn on a few of their faces. The boy with
food all down his front nudged the girl next to him and pointed openly at Harry's forehead.
"Are you going to ask me to dance at all?" Padma asked him.
"No," said Ron, still glaring after Hermione.
"Fine," snapped Padma, and she got up and went to join Parvati and the Beauxbatons boy, who conjured up one of his friends to join them so fast that Harry could have sworn he had zoomed him there by a Summoning Charm.
Having stated that, there's definitely a feeling that Rowling did deliberately "feminize"/"masculinize" the two schools (even aside from the fact that the mentions above - by their rarity - give the impression of a gender imbalance in the delegations):
the names themselves ("beaux" means beautiful in French and is a decidedly feminine word to use; and "drum" and "strang" are both German words that have masculine - or at least aggressive - implication - never mind what one gets if they are mixed into "drang").
the locales (French vs. Norse)
the headmaster/mistress gender
as well as the description of the school (Drumstrang is cold, with no frivolities or amenities, no fires for warmth; and Beauxbatons is a "palace" with statues, wood nymph quire etc...)
Also, the choice of "main" characters - who were not merely TriWizard champions, but ALSO pretty much hyperbolized their gender (Fleur's Veela feminine super-charm, and Krum's "tall dark and handsome" sports hero figure attracting all girls during the year); but they also romanced the important heroes (Fleur with Bill Weasley and Krum with Hermione).
All of these seem to imply that this was intentional characterization on Rowling's part, even if she did include snippets proving them to be co-ed, at least technically.
As to WHY this was done, JKR never seemed to explain in all her interviews, other than mentioning that she once taught at an all-boy's school in France in an unrelated answer.
However, plenty of real life private boarding schools - which magical schools are patterned on - are (and especially were in the past) not co-ed.
Given the amount of distraction amour caused at Hogwarts to the detriment of learning, one can certainly see the appeal of a single-gender school.
The movies probably went all-hog with this because it made for a reasonably stunning entrance visuals.