Yes, brutal can proc when Joy doesn't, but counting Joy as 50% proc rate, then brutal has a chance to proc 50% of the time, effectively making the 5% proc rate a 2.5% proc rate.
Now, a 2.5% proc rate at 100 attack rounds of a normal weapon would be
100 attacks vs 102.5 attacks
102.5/100 = 2.5% increase
but w/ joy, we have to account for it's extra attacks, too, in the total number of attack rounds.
@ 50% proc on joy, 100 attack rounds makes for 150 attacks + 2.5 from brutal.
Now we have 152.5 vs 150
152.5/150 = 1.67% increase
If you're subbing war 10% becomes 5% DA rate.
w/ joy 155 attacks in 100 rounds w/ joy, 157.5 w/ brutal
157.5/155 = 1.61% increase
Now w/ diabolo's and assuming 85% hitrate, you'll gain 1.5
1.5/85 = 1.76% increase
At 85% hitrate, 3 acc > brutal with joyeuse