I love making pizza. And I've been reading this book "The Neapolitan Pizza", which is supposed to be, as they describe it in the subtitle, "a scientific guide about the artisanal process". I was fascinated by the amount of technical information available in there. Though, I was in shock when I read the following, the authors were talking about wood fired ovens: "The concept of wood giving a particular aroma is false: there's no transfer of aromas from the wood to the pizza". I remember getting some bread from a place called (now ironically) "Firehouse", great bakery. And I remember feeling this fantastic taste of a smoked delicacy in their loafs. Have I been fooled by my brain? I'd really expect that at least tiny particles of burnt wood and other chemicals from the smoke to somehow land on the baked good and give that a taste, why that doesn't happen? Or is the smoked flavour something different from the wood flavour? 
The book is correct, for two reasons:  Wood-fired pizza ovens are not smokey, instead having very good draft in order to allow maximum hot fire burning. A pizza is in a Neapolitan pizza oven for 60-100 seconds, which is not enough time for something to absorb smoke flavors, even if the oven were smokey.  The reason to use a wood-burning oven for your pizza is the intense heat of 450C or more, which is required for many Italian pizza types. That heat is harder to achieve in electric or gas ovens. If you get any flavor of wood at all, it would be only from any ash stuck to the oven floor. However, where you noticed the smoke flavor was from bread, which cooks for up to an hour, in a much lower heat. Given that amount of time, a bit of smoke getting into the crust is a lot more possible. 