How wide is the usage of causative (使役) す/さす comparatively to せる/させる?
Historically, 「す/さす」 is older than 「せる/させる」.
Just like many other pairs of older and newer words/phrases with the same meanings, the older forms are used more often and actively in Western Japan than in Eastern Japan. (That is if you know anything about Japanese history.)
To say "What are you making me say?", for instance,
Tokyoites would tend to say:
while Osakans would be likely to say:
In schools, however, regardless of what part of the country we are from, we all basically learn to use 「せる/させる」 in "Standard" Japanese. You would rarely, if not never, see or hear 「す/さす」 used in the media these days.
Thus, both forms may be used equally often "at homes" across the country, but in school, business, media, etc., 「せる/させる」 would be the dominant form.