Ah I was basing my deployment statement on the wiki, which must be outdated.
http://www.eu4wiki.com/Land_warfare#Unit_deployment
Specifically: If there is enough infantry to fill the entire first row:
Deploy all infantry in first row, except the outer positions in the amount of cavalry available but not more than 6[[this amount is made up]] (3 left and 3 right).
Deploy up to 6 cavalry in first row at the sides of the infantry.
Deploy all artillery in the second row.
If space left in the second row, deploy all remaining infantry in the second row besides the artillery, but leave the outer positions in the amount of cavalry available but not more than 6[[this amount is made up]] (3 left and 3 right).
Deploy all remaining cavalry in the available space in the second row, beginning with the positions behind the cavalry in the first row and then going inwards to the infantry.
EDIT: I looked over that thread (briefly, first & last page) and didn't see any commentary that cav is worse per regiment than inf, just that it is less economical per ducat.
What I'm asking is whether, per regiment, cavalry are superior to infantry (so long as you don't have insufficient support).
E.g., with combat width 30 and all modifiers equal, which army wins?
24/16/30
34/6/30
(Does the answer change depending on tech level? If so, what's the inflection point?
If the answer is the inf heavy one wins because it causes enough casualties to lead to insufficient support, double the # of inf & cav in each army til that no longer happens.)
And nouli--it sounds like you are saying that for deployment, it would be 15 infantry and 15 cavalry deployed in the front line of the first army, not 24 + 6?
EDIT 2: I read more of the thread, I see some tests in there

.