Techniques like Life Cycle assesment (LCA) can be used to answer this kind of questions, but these techniques often need to make many assumptions.
Some example studies and their references can be found in this presentation. It cites 20 studies that state that conventional agriculture has lower green house gas emissions than organic agriculture, vs 8 that state the opposite.
However in my opinion: if you would use a technique like LCA to find out the best management for a specific piece of land, you might end up with eg a agroforestry system which uses chemical fertiliser. This is not 'conventional' agriculture. It is not 'organic' agriculture. It is a combination of techniques without being dogmatic.
In fact, if you compare such a system vs a 'organic' system, it would have the same environmental impact if no changes are made, but if some techniques which are not allowed in organic farming are used wisely the environmental impact (according to the metric you chose) may decrease. A clever usage of all available technologies, some of which are not allowed by organic farming, should therefore always score 'better' than organic farming, and also better than 'conventional' farming.
You may also want to read this Nature article, which actually supports the same claim: Urban myths of organic farming (free download)
Organic agriculture was originally formulated as an ideology, but today's global problems — such as climate change and population growth — need agricultural pragmatism and flexibility, not ideology.
This does not mean that some of the issues that organic farming tries to tackle are not real. I like some of the research of Jules Pretty, who has been looking to external costs of agriculture: external cost UK agriculture. (Free download )