Typical you need to use a bottom plow to turn over soil to actually kill weeds to the root level. Discing would need to be pretty deep. You have all the negative aspects on soil health when you disk as well. If you want to understand the aspects of no-till verses tillage, I suggest watching some of Ray the Soil Guy's videos. You will probably notice better results faster using traditional tillage. The problem is that it is not as sustainable over the long run and requires much more input.
With traditional tillage, you deplete the soils natural cycle and try to compensate for it by adding lots of fertilizer. Year after year, as the soil biology crumbles, it can take more and more inputs like fertilizer and over time the soil degrades to the point your yields begin to drop. That is one reason old-time farmers would "rest" fields for a year or two if they could economically.
So, if you want to compare no-till to traditional tillage, you can't compare one field you plant this year to another. You need to plant the same way in the field year after year and compare how the fields perform in 10 years.
Having said that, folks are in lots of different situations. There are times when tillage is needed, but they are generally infrequent special situations. Throw and mow may work better in some situations than others. A not-till drill is a great option if you can afford one. Also, there are downsides to using herbicide for weed control.
I'm personally moving more and more to minimizing tillage (both depth and frequency) to the extent I can. I'm also becoming more tolerant of weeds and spending more time looking at the big picture.
Thanks,
jack