It has already been noted that "in every way" sets a standard that is, effectively, impossible to meet. In this case, there is a really easy point that goes to monoculture right off - harvesting a monoculture is easier, more efficient and by those measures arguably "better".
But here is the problem. Your question is liking asking "what color is the sound of thunder?" What does that mean, you ask
You are asking for a comparison as to which is "better" between two things that are, really part of two very different, and I believe largely incompatible, paradigms.
Up the thread it is suggested that the fact that techniques advanced by permaculture today are (many of them) old techniques that have fallen out of favor because they are inferior to modern techniques that have replaced them. That idea uses profit as a measure of quality to determine 'better'. That is not a very good measure of quality, for starters, and it is very well established that modern agricultural methods are only profitable by ignoring vast costs that the industry pushes off of its books and onto the permies. Soil erosion is a cost, water pollution is a cost, dead zones in the oceans are a cost, elimination of ecosystem diversity, stability and resilience is a cost - and there are arguably many others, but those are plenty to start with.
Industrial agriculture makes loads of money for some people in its heirarchical structure. But those people are not typically the farmers producing the source product. So, even with the currently 'profitable' system, which is largely profitable by displacing enormous costs, farmers are not making large profit margins.
If you compare large scale organic to "conventional industrial" agriculture, the biggest difference, I think, is in the character of the inputs. Both run large monocrops with high degrees of mechanization, processes optimized for mechanized handling and long distance shipping with (relatively) long term storage, both push costs off onto the public (land erosion probably the big one they have in common). Both use lots of fertilizers and pesticides, just different chemistry.
Permaculture approaches seek to minimize the inputs coming from off the property. Big cost advantage there for the Permaculture side. Permaculture addresses the costs that the other guys push off their balance sheets and even manages to turn some of the conventional costs into potential income streams, or at least make them beneficial to the permaculture farm and cost reducers rather than expenses. That's a pretty significant benefit of permaculture, but it will not appear as one when you compare balance sheets - remember, the costs are not showing up on the conventional balance sheet in the first place.
Permaculture systems are not optimized for mechanization, nor for transport, nor storage. Permaculture's ethics don't encompass using all that energy to transport lettuce from California to Indiana, etc. Permaculture envisions a distributed production system, not a centralized production process with a widespread distribution system. In economic terms, ignoring the costs of operating the distribution system (not a cost to the farm production system, so not on that balance sheet), it is more efficient to run one large streamlined operation than many much more labor intensive operations. But that is a false accounting, the transportation costs are part of the system.
Permaculture farming will absolutely require more human labor than monocrop production systems. Monocrop systems are optimized for mechanization, minimizing human labor. Even where the mechanization is less (not all crops can be harvested by combine), the monocrop system is designed for efficiency in terms of the costs they acknowledge on their books, such as labor. Diverse polycultures take more labor to harvest than do monocrops. Different priorities are being maximized between the systems.
The bottom line, as I see it: Permaculture is part of a paradigm where the economics include all of the costs of a system of operation, and where cost/benefit analysis looks first at ecosystem impacts, not at dollars.
Current industrial agriculture (organic or not) is part of a paradigm where costs of a system are pushed off, buried, ignored, denied; and where cost/benefit analysis looks first and almost exclusively, at monetary measures of success.
Neither one can compete on anything like an equal footing with the other when placed in the other system's appropriate paradigm.
Which paradigm is better? One where environmental costs are shoved off corporate balance sheets and we are all left to pick up unimaginably large tabs for their actions? Or one where environmental costs are factored in, where the approach even works to convert some of those costs into benefits (see, for example, conventional manure lagoons versus permaculture approaches to animal husbandry and waste management), and society as a whole does not get stuck with the tab for environmental clean up, largely because the production approaches do not produce negative environmental effects?
Which is better - healthy for the Earth? or makes a profit for Syngenta's shareholders?
I know which paradigm I prefer.