What is different between $\frac{1}{1+\lambda x}$ and $\exp{(-\lambda x)}$

Question

I want to choose a function $f(x)$ which has properties: $f(x)$ closes to $0$ when $x$ goes to $+\infty$ . I have two option for that

1. $f(x)=\frac{1}{1+\lambda x}$, where $\lambda$ is tuning parameter
2. $f(x)=\exp{(-\lambda x)}$

What is different between first and second options? Which one is better?

As my knowledge, I think main different is that fraction function is more smooth and gradually reduce than the exponential function. Thank all