Monte Carlo Distribution: Normal Vs. Laplace

What is the difference between a normal and Laplace distribution in Monte Carlo simulations? Which one should I use?

Although many random variables exhibit a normal distribution, equity and fixed income returns have exhibited a Laplace distribution over the past ten years. A Laplace distribution has fatter tails than a normal distribution, which increases the probability of extreme events relative to a normal distribution. In statistical terms, a Laplace distribution has kurtosis of 6.0, while a normal distribution has a kurtosis of 3.0. More information on these terms can be found here:

Laplace Distribution-
Are Stock Returns Normally Distributed?-

WealthTrace Blog Post- Monte Carlo Retirement Simulations in WealthTrace