I believe you are looking for information on "sustainable agriculture". There are many aspects of production in agriculture like: fertilization, irrigation, pesticides and (no-)tillage. One can try to calculate the carbon foot-print of food (beware of the calculations, they might be misleading).
Crop rotation is helpful in sustainable agriculture but it is not always available, making traditional (industrialized) agriculture the only viable option. The economic aspect is also important. Agricultures need to grow the food and they will grow it only if the make money from it. Organic and sustainable agricultural products get a premium for being cultivated that way but these premia go down as more farmers use them.
The question "How the yield is affected by the agricultural method" is a broad question that attract interest in research. We need to break it down to: What is yield (biomass? marketable product?) and what is agricultural method.
A great study conducted in Ontario, Canada by Stonehouse et al, 1996 compares the herbicide treatments in 3 types of farms: conventional, reduced input and organic and the yield, investment and profit for three crops: grain corn, beans and cereal grains. The data arrives from self-reported data by the farms. This is not a fully randomized experiment and there are many differences between farms (size, investment, land) but precautions were taken to reduce them. Reduce input farmers used less herbicides than the conventional ones.
This is the table from the article
There reported more information as profitability but since this study is from 25 years ago I believe it is no longer relevant.
This study is only one showing the complexity of the subject and one of the methodologies employed. One can write various books about the subject so I hope this post gives you the direction that you needed