I think, in general, we have a pretty poor understanding of how various foods interact with the human body, particularly foods that trigger hormone production (as many high density proteins, like meats and non-tofu soy products, do). So, I would probably agree that a well-balanced vegetarian diet probably does lead to a more balanced day-to-day emotional life, which helps with concentration, wakefulness, and feeling good about what you're doing with your life (which I find is the single most important aspect of productivity for me).
I certainly encourage folks to give it a try, and see how it works for you. But do some reading first. There are some non-intuitive aspects that throw new vegetarians for a loop, and make the experience less than satisfying. For example, soy proteins of some types, while they seem like a high quality protein, are actually rather hard for your body to deal with. Tofu, on the other hand, which is processed similarly to cheese, has had those hormone-related proteins broken down into a form very friendly for your body.
I've also known people who've become vegetarian and gained weight (which was not my experience, as I lost about 15 pounds within months of becoming vegetarian without trying), because they've become carb-o-terians or bean-and-cheese-a-terians. Even if you rule out a whole class of (predominantly) unhealthy food in the form of meat, you can still eat a phenomenally unhealthy diet. And being unhealthy is bad for concentration (among other things).
That's a fascinating area all by itself. I read a couple of years ago about a study in hyperactivity and (while it's not classic double-blind, etc) the anecdotal examples presented were interesting. In one case, a woman with identical twins (who were hyperactive and very unruly) started feeding one on "real food" rather than the processed stuff that many busy parents rely on. Two weeks later, there was a huge difference in behaviour, in the way that you might predict. I'll see if I can dig out a link.
A friend of mine is a school-teacher, in a really rough school. They just banned all forms of soft drink, and he says that has, in itself, made a big difference with discipline. Basically, kids who were getting tanked up on sugar and "bouncing off the walls" are now noticeably calmer and easier to manage.
Religious debates to one side, it's easy to forget that our bodies are just a bunch of chemicals, so the chemicals we put in are bound to make a difference. Thanks for relating your experiences :)