There are both advantages and disadvantages to using pizza screens.
A key advantage to using pizza screens is that you donít have to heat the oven as long, only to an ambient temperature of around 425+, which will usually only take about 12-15 minutes in a standard home oven. This can be a real advantage in the summer when it is hot and the last thing you want to do is crank up the oven for an hour or more to preheat the stone and endure the residual heat of the stone for several hours more as it cools down. It is also easier to load a pizza into the oven when the pizza is on a screen versus using a peel/stone combination. Some pizza operators who have deck ovens will still use screens simply because it is easier to use screens to dress pizzas than to have to train workers, especially new hires, to hand stretch skins and use peels to load the dressed pizzas into the oven. So, the oven load error rate goes to about 0, except for the occasional case where a pizza sticks to the screen, especially when high hydration doughs are used or where workers let a dough sit too long on a screen before saucing and dressing. Even in a home setting, you canít dilly dally when dressing a pizza on a screen.
Since a screen will produce a different bottom crust characteristic than will a deck surface, some operators who use screens will ďdeckĒ the pizzas off of the screens onto the deck surface toward the end of the bake to get a bottom crust more similar to one baked entirely on the deck surface. In reality, many pizza operators who use screens in conjunction with deck surfaces do so because their deck ovens are malfunctioning, or they are using the wrong ovens, and incapable of achieving the desired balance between the bake of the tops and bottoms of the pizzas (usually the bottoms are burned). The screens lift the pizzas off of the surface by a fraction of an inch, which helps achieve a better top and bottom balance by allowing the pizzas to bake longer before the bottoms can overbrown.
An additional advantage of using a screen is that you can use sugar in the dough formulation and reduce the likelihood of the bottom of the crust browning too quickly or burning because of caramelization of the sugar when the dough comes in direct physical contact with the hot stone surface. This usually becomes a problem in a home setting when you are using better than about 3% sugar (as a percent of formula flour).
A point to keep in mind is that screens were developed mainly for conveyor oven use, for essentially most standard pizza styles (but not deep-dish). As such, screens will not produce the same bottom crust characteristics as a crust baked on a deck surface. As you may have noted, the NY style pizza is traditionally one baked directly on a hot deck surface, which is what we try to simulate when we use preheated stones in a home oven. You will almost never see a NY pizza joint in New York City use a conveyor oven. Using screens in a conveyor oven to make a NY style will get one about 80-85% of the way home in terms of equality of bake. Oven designers have been working for years to close that roughly 15-20% gap. Recently, pizzatools.com, through its Lloydís division, has designed a special perforated anodized disk that is said to produce results in a conveyor oven that cannot be distinguished from the results using a deck oven. I donít believe it is available yet at the retail level, but rather is being trialed on a limited basis by operators. Tom Lehmann helped design the disk. Disks, in general, are increasingly replacing screens, even though disks are orders of magnitude more expensive than screens. Screens need to be seasoned and sometimes cleaned and reseasoned, and they are prone to falling out of round over time, having staples come out, and having fragments of the screen finding their way into pizzas. Health departments much favor disks over screens. Of course, in a home setting, these are not problems you are likely to encounter with low volume usage.
As I was composing this message and ready to post, I see that Christopher offered his thoughts on this matter. He makes a good comment on another benefit of using a screen in conjunction with a stone. I frequently use the same combination, for the same reasons as given by Christopher.