While both materials do have slightly different properties, either one will work in the scenario mentioned. In-fact, any sling with the UIAA stamp of approval will likely have a working strength of 22kn - more force than you will ever be able to generate by falling if being belayed by a rope.
The latter part is important, because the rope (among other things) is what will absorb the energy of your fall in this scenario, not the sling. Again, just to elaborate: Your rope is designed to catch the impact of your fall, a sling is not. In the videos presented by DMM you can see what happens when the sling is forced to absorb the impact of a fall, and it's not pretty.
The question of what material to choose from will depend on the conditions more than anything else. Materials like Dyneema are lighter, and won't absorb as much water as Nylon in wet weather, making them the ideal choice for applications where weight or weather is a primary concern, like mountaineering for example. They also have the lowest melting point from all the climbing fabrics though, so will probably need replacing sooner.
On the other hand, Aramids (Technora, Kevlar etc..) can be just as strong, and have the highest melting point of most materials, upwards of 500C celcius. This makes them perfect for those long rappels, or hauling and rescue scenarios like firefighting. They also happen to have a much worse shelf life when it comes to UV degradation (from exposure to the sun) however. Nylons fall somewhere in between on both counts.
Ultimately, any UIAA approved sling can be expected to hold the force of a falling second when being belayed by a rope; and if switching leads, you can always use the climbing rope itself to tie an anchor also.
Here is a link to the properties of some common materials as further reading: http://www.marlowropes.com/technical/physical-properties.html
Beyond material properties, additional preferences will come from application, and which fabric will be easier to work with. For example, knots are easier to untie from thicker material, so Nylon will be a better choice if you are putting in lots of knots.