They can be different. "Simple is the best" uses the definite article "the." As such, one could be making reference to three choices; for example, "I utilized three methods of construction in my project: difficult, moderate and simple. I found that "simple is the best." So... based on a limited number of choices, "the best" was the simple one. On the other hand, "simple is best" could make reference to an overall concept. For example, "when it comes to my outlook on a way of living life, 'simple is best'."