The benefit is more efficient cooling.
To create positive internal pressure means to force more air in to the case than remove it but this means you could have a lot of hot air swirling around inside the case waiting to be removed by minimal exhaust fans.
To create a negative pressure means to exhaust more air than you force into the case. This is great cause your forcing in fresh air but your removing it quicker together with any hot air given off by the internal components.
Imagine being sealed in a hot room. You would prefer more exhaust, to get rid of the heat, than lots of fresh air coming in and a piddly little exhaust. Don't get me wrong, you want both but you'll want more exhaust.
This works best with plane side panels giving a perfect front/bottom intake, rear/top exhaust design.