Sled bases provide an easy weight distribution and don't get stuck in ruts in-between cobbles and other uneven flooring or sink into grass in the same way that a four-legged chair would. This is especially useful for chairs to be used on grass that is often damp.
Many of the other benefits of specifying a cross sled base derive from the fact that they are usually made of metal though wooden variations do exist. Metal is the strongest material for chair and stool construction. This is because a welded joint is as strong as the metal itself and metal will not snap in normal circumstances. Simple metal work also tends to be cheaper than wooden equivalents.
In terms of finish, painted metal also chips less than painted wood (it can still, however, chip). Also it's good to be aware that not all metal chairs are treated for outdoors use even when powder coated, so can’t all be used outside. To be on the safe side, check with the individual product info every time you specify a chair for outdoors use.
Downsides to specifying cross sled bases
All sled frames have a slight side flex which sometimes puts people off specifying them as they appear to be less solid. This is completely not the case and they are still extremely robust despite the flex.
Metal chairs usually stack much higher than chairs made from other materials because the frame is thin and strong. Traditional sled bases are often used for meeting rooms, conference rooms and education environments as they stack highest and can be connected together using connector pieces between legs. However, chairs with a cross sled base can't stack because they're joined at the bottom.
Similarly, traditional sled bases slide in easily under tables but cross sled bases aren't going to glide in quite the same way because of the X in the middle.