I don't think that's really Occam's razor. It's not just about picking what's simplest, but on what makes the least amount of wild assumptions. I'd say a logarithmic curve makes less assumptions, and an exponential curve makes too many.
I guess you mean logistic, since a logarithmic curve is identical to an exponential curve with switched axes. A logistic dependency is more complex, making more assumptions, by all counts:
- A logistic dependency is just like an exponential dependency with saturation accounted for. The former assumes there's saturation, the latter doesn't.
- The formula is more complex to write, the curve is more complex to draw.
- When generalised, it has more parameters.
- The exponent is the
mathematical function. It's pretty much the simplest and it is pretty much everywhere.
- And most of all: A logistic function has an exponential function in its definition.
A logistic curve is simpler than an exponential curve in the same way that crashing on Mercury unaided is simpler than landing on Mercury with retrorockets – not at all. It's the latter that assumes the rockets will actually fire.