This is something I've been thinking. While it is agreed that Lambda Calculus is equivalent to a Turing Machine in power, is it actually so? Church Numerals are not very space efficient and I'm not aware of any better way to represent numbers using the LC. This leads me to the intuitive conclusion that, while, theorically, LC is as powerful as a TM, there is a natural limit that states that a program in LC will never be able to compute natural numbers as fast as a TM, given a physical world and limited resources.
Now I've throw many ideas and it is hard to define most of what I'm saying formally, but does that intuition make any sense?