When pureeing tomatoes for a fresh tomato sauce, should you throw out the juices or not?
I would not throw any part away.  There is flavor in all parts of the tomato, particularly the interior (see my comments under an alternate response below). Plus, if you are pureeing first, don't you think the flavors are being mixed, resulting in the loss of at least some flavor if you remove some part of the mixture? Simmering does indeed allow water to evaporate, but, in doing so, it concentrates flavor.  How much flavor is gained or lost?  I am sure this will depend on the variety, seasonality, and ripeness of your tomatoes.