The linked question in comments makes some general points about dedicated pizza ovens.
However, to address the final question about temperature differences, the general answer is that it depends on the style of pizza you'd prefer to make and the dough/topping characteristics. Some doughs and pizza styles are designed to be cooked at lower temperatures for longer times. If you like thick-crust or "deep dish" style pizzas, an oven that is too hot can burn the crust and/or toppings before the pizza is fully baked.
Assuming that you intend to bake thin-crust pizza, generally the hotter the oven, the better the results. Traditional Neapolitan pizza has official regulations requiring a minimum cooking surface temperature of 430°C, with an oven temperature at a minimum of 485°C. (Note the Fahrenheit conversion temps are swapped in the document from what they should be.) They are also required to have a bake time less than 90 seconds.
It's doubtful that one could achieve that in a traditional home oven or even most dedicated pizza ovens for home use. There are lots of minor changes that happen with such fast cooking, such as the slight charring patterns on the bottom of the crust and on the edges, more significant oven spring, more rapid drying of the dough which alters the texture, etc. However, by varying the dough composition (type of flour, other added ingredients besides yeast, salt, and water, such as oil/fat or sugar), one can create other styles of pizza that have some characteristics baked at lower temperatures. Some people, for example, like to put a little sugar and oil into their crusts to change texture and flavor -- baking those pizzas at 500°C would likely produce excessive browning and charring.
A final thing to note is that temperature is often not as important as heat transfer rate in achieving pizza results. Many people recommend making pizza on a preheated stone to increase the heat transfer rate. However, in a home oven with a maximum temperature of 250-285°C or so, there's only so much you can do to raise the temperature of your cooking surface.
On the other hand, you can increase the rate of heat transfer into your pizza by doing things like (1) using a large thick hunk of steel to bake your pizza on (which can transfer heat much more quickly than a stone) and (2) turning on the broiler after the oven has hit its maximum temperature, which will increase radiant heat transferred into the top of the pizza (beyond that conveyed from the air in the oven). The combination of maximized heat transfer on the top and the bottom of a pizza can bake the pizza a lot more quickly and achieve results that would normally require a much hotter oven. It won't quite get you to Neapolitan-style pizza in a home oven, but it can get significantly closer.
(I can bake a pizza in roughly 3 to 4 minutes in my home oven using these techniques, a lot longer than 90 seconds, but significantly less than the 8-10 minutes or longer most people take with standard stones. But the major noticeable differences aren't the cook time -- but rather significantly increased oven spring, better texture, and better browning.)