Personally, I define pizza broadly. For example, I'd say the mushroom flatbread served at The Redhead can certainly be considered pizza.
Any trip to the Yeminite Food Bar should include a taste of both. The only complaint is that they are not particularly filling and at 25 shekels ($7.00) each, they are slightly overpriced. Not surprising since Safed is a bit of a tourist trap. I spent a total of $14.00 on my two wraps and was still hungry. Even 20 shekels each would be more reasonable. One wrap is just the right size for a snack, but even two can't quite pass for a meal.
The man who works there said that he'll occasionally try some new recipies depending on what's in season, but that in general these are his two staples. As previously mentioned, one thing that any food establishment in Israel has going for it is the quality and freshness of the ingredients. Yeminite Food Bar was no exception.