To summarize: Engineer-trained managers - in the absence of other trainings (such as MBA) can be good at certain settings, bad at others.
Engineering fields tends to attract personality types that focus on problem solving (both tactical and strategic) and project-based planning. These types are generally quite reliable and tend to be direct and honest about their assessments (ie, they don't like to BS). They are very good at detecting and averting crisis before it can happen. At the same time, they are more likely to ignore the politics aspect of the workplace. They may also not be particularly creative, and could perform poorly in customer-facing situation due to lack of social skills.
As a result, a department ran by engineer-type would most likely be highly efficient. There will rarely be an 'off day'. Everyone will likely know their job function, what they are required to do today, this week, or even next month. While one might expect that this is the ideal manager type for any situation, the reality is that this type of management style could be disastrous in the sales or marketing department settings - where managers are generally expected to adapt to a much more dynamic working environment that is driven by competition and customers' demands (both of which can change on a day to day basis), and creativity is valued far more than efficiency.
Even in the case where an engineering type is managing productions-related department, his/her inability to handle office politics could result in the department being underfunded, or stonewalled by other departments (thereby making life extremely difficult for projects that require cross-department initiatives). I have seen excellent technical managers unwittingly ran his entire production department to the ground because he simply couldn't (or wouldn't) protect his subordinates from office politics. This happened not just once but TWICE in my career. In both cases his subordinates (all very good, skilled people) simply left the company because they were being constantly bullied or taken advantage of by other departments to the point that they couldn't get any work done.
Subsequently, engineers who wants to become managers - both inside or outside of productions/technical related fields - are generally advised to go through additional training such as an MBA to develop the necessary soft skills to cope with these situations. Some engineers may already possess the 'soft skills' and could therefore make the quantum leap without the need for further education. However, these tend to be few and far between in my experience.
Conversely, an MBA on its own does not produce good managers. Without proper problem solving skills and ability to think and plan ahead, an MBA-trained person is a little more than a politician who can speak eloquently but can never deliver on his/her promise. I.e. an empty shell that just happens to look good from the outside. Unfortunately, too many of these are running around consultancy and wall street firms these days and creating all sorts of troubles. And one wonders how the 2008 financial crisis happened!
Any person who can combine both hard and soft skills would make very good managers/leaders. I would imagine these people are worth their weight in gold to any companies!