Yes boiling sprouts does kill some of the nutrients in the sprouts so the boiled sprouts are not as healthy as they would be if you ate non cooked sprouts.
Still though the boiled sprouts do still retain some of the nutrients as not all nutrients or vitamins are killed off by the boiling process of the sprouts.
So even when you boil sprouts the boiled sprouts are still healthy for you.
The only way I will eat sprouts is by boiling them because although sprouts can be eaten raw the boiled or steamed sprouts taste much better and are easier to chew and digest.
All vegetables do lose some nutrients when you cook them by steaming or boiling them but the vegetables are still pretty healthy for you.