Many of the "Simple English"-language articles on Wikipedia are better (IMHO) than their English counter-parts. Perhaps the best would be a mix of both, eg the introduction to:
https://simple.wikipedia.org/wiki/Fraction_(mathematics)
"A fraction is a number that shows how many equal parts there are. When we write fractions, we show one number with a line above another number, for example, (...) 1⁄4 or 1/4. The top number tells us how many parts there are, the second number tells us the total number of parts.
The top part of the fraction is called a numerator. The bottom part of the fraction is called a denominator. For example, 1/4: The 1 is the numerator here, and the 4 is the denominator."
vs the "English" one:
"A fraction (from Latin fractus, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters. A common, vulgar, or simple fraction (examples: 1/2 and 17/3) consists of an integer numerator displayed above a line (or before a slash), and a non-zero integer denominator, displayed below (or after) that line. Numerators and denominators are also used in fractions that are not common, including compound fractions, complex fractions, and mixed numerals."
> Is it that you think more about what you're saying?
I think this is one important reason - and key behind all good writing. Using a limited vocabulary is one way to force yourself to do that.
It's also a way to force yourself to examine what you write, and make sure you actually use words you understand, and not stray too far into your passive vocabulary and accidentally introduce ambiguity because you think you are using more precise words than you actually are.
I would also say that, while rich language can be fun, most writing can benefit from being simplified. Not everything needs to read like Paradise Lost.
In the words of Hemmingway: "Don’t get discouraged because there’s a lot of mechanical work to writing. There is, and you can’t get out of it. I rewrote the first part of A Farewell to Arms at least fifty times. You’ve got to work it over. The first draft of anything is shit. When you first start to write you get all the kick and the reader gets none, but after you learn to work it’s your object to convey everything to the reader so that he remembers it not as a story he had read but something that happened to himself."
(Here with more context, than the traditional quip: "The first draft of anything is shit.", in order to emphasize that the point is that everything needs to be reworked).
On a similar note, I recommend that everyone who writes (ie: everyone) read: "On Writing Well" by Zinsser (himself a propoment of revisions, the book is in its 30th edition):
http://www.amazon.com/Writing-Well-Classic-Guide-Nonfiction/...