Imagine a bucket full of large stones. You fill it. Then you shake it and now the level of stones went down and you can fit more in. That is basically what the plow and disc is doing to your ground I.E. compaction. In a true no-til environment, yes you still have the rain trying to work the air out of the dirt but you have decaying root systems, worms and other organic matter dispersed through the soil all working to keep it mellow. There are some types of ground that no-til will not always work but in many cases it will. Normally it takes a few years for the soil to get stabilized to see the benefits of no-til.
That said, if I was a big gardener I would probably still do tillage just for the sake of easy planting by hand or push-planter. I don't think you are going to find the tiller or plow much ahead of the other on the compaction issue, I myself would have the tiller as it normally leaves a nicer seedbed than plowing and discing and it's only one trip over the field.