I'm not sure about the difference in temperatures, but regarding the pros and cons of the kinds of baking possible in white and black ovens, one thing to consider is whether client was really looking forward to making pizza. If so, I'd recommend a black bake oven over a white oven. Not because of the temperature - excellent pizza can be made even on a 550 F hearth if you don't mind waiting five minutes for it to bake - but because the presence of a live fire enhances the flavor. A live fire also enhances the experience of making pizza, makes it somehow more enchanting and memorable.
In general, the main downside to white ovens is just that: the lack of the option of live fire and embers on the hearth. Flames and embers deliver different types of heat and unique baking environments that cannot be achieved in their absence, no matter the temperature. White ovens are great for many cooking and baking methods: baking, roasting, braising, low and slow cooking, dehydrating. But black ovens can do all that stuff just as well. The benefit of the black oven is that it expands your possibilities to include the elemental pleasure of baking and cooking with fire.
For bread and other baked goods that are baked with retained heat once the fire is removed, the main downside of a black oven is that you only get one shot to heat the thermal mass per bake cycle. If you find the temperature is falling too quickly, it is not easy to jack the heat back up or to alter the rate of decline. There are effective ways to prevent or deal with this, though:
White ovens don't have this issue because they can be re-fired during or between bakes, making it possible to recharge the mass and maintain temperatures in the baking chamber as necessary.
Grey ovens offer the benefits of both black and white ovens, without the downsides of either. They have maximum flexibility due to three different ways to deliver and maintain heat in the baking chamber: an external firebox with channels that direct the flue gases around the baking chamber like white ovens; the option of directing the flue gases into and through the baking chamber; and the ability to build a fire directly in the baking chamber like black ovens. What's not to love? I want one! (See clarifying note below.)
Wall thickness (thermal mass) is most critical with black ovens, since the client only has one chance to charge the mass with heat to last an entire bake cycle. There should be enough thermal mass to store the amount of heat the client will want to use, but not more than the client will be able to thoroughly heat in a reasonable amount of time, with a reasonable amount of fuel. An important consideration is whether the oven will cool to ambient temperature between firings. Commercial ovens and residential ovens that are used on a frequent basis can have lots of thermal mass because they never cool down to ambient temperature between firings, so once the thermal mass is initially charged the subsequent firings won't need to be too huge, only enough to 'top it off' rather than re-fuel from empty. In contrast, an oven that will only be used occasionally can be expected to cool to ambient temp between firings, so every firing will have to fill up from empty. In this case it can get really costly and frustrating for the client to have too much thermal mass.
Too little thermal mass can also be a real bummer in a black oven, but it is not that big of a deal in a white or grey oven, since heat can be added to maintain or raise baking temperatures as needed.
* Steph is a member of the Masonry Heater Association and is married to Richard Miscovich who is a bread baker, currently teaching artisan bread baking at Johnson & Wales Culinary School
As I wrote it I was wondering if I was using the terms black, white and grey correctly.. Here are the definitions I had in mind:
Black oven = firebox and baking chamber are the same thing.
I am more familiar with stand alone ovens rather than those built within a heater, so not sure how well these definitions fit in the context of heater oven designs.
Tom you are right, a grey oven as I defined it is essentially a black oven, only difference being that this black oven also has an external firebox. And the external firebox is the main source of heat, if only because loading, waiting for the burn to finish, and completely raking out the baking chamber each time you want to re-fire is more trouble and time-consuming than just stoking up the an external firebox. Also, you are correct to identify the compromise regarding adequate mass and adequate insulation when the design includes walls thin enough to absorb heat from the outside surrounded by dead air space when the external firebox is not in use.
As I understand it, the way around this is to adopt a different firing method--much more frequent, although small, re-firings in the external firebox than we are accustomed to in the familiar thick, insulated walls of our high mass retained heat ovens. Antoine returned from France with tales of numerous bakers he visited who use ovens of this design (with the removable cast iron guelard gooseneck vent to direct the exhaust gases into the baking chamber from the firebox below), and he describes them re-firing a short, small but intense burn in the external firebox between each load of bread! The bonus is that you can just keep baking and baking as long as you care to, re-firing with brief hot burns as you go.
My hunch is that wood-fired bake ovens in North America will evolve to incorporate this feature while retaining the best of what we love in our current designs. That's where all you heater/oven masons come in! The improvements in oven design this group has contributed over the last couple decades have made a huge positive impact on the wood-fired oven bakers in this country, and thankfully there is no end in sight. We salute you.