One benefit is reduced cooking time since you need to evaporate all the juices before the tomatoes start caramelizing. On the other hand, wont these juices contain flavor you might waste if thrown away?
How much flavor will I miss out on if I throw the juices?
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.
I would not throw it out! Season it and freeze the extra into ice cube trays and pop them out when frozen and place in any freezer container. When you need a punch of flavor to anything you make in the future you will have a nice addition! I use these "broth" cubes to season rice, soups or sauces that I make all year long. Just an idea.
The watery juice on the inside of the tomato doesn't have much flavor once cooked down, the good stuff is the flesh. When making a tomato sauce the recommended process is to scoop out and discard the seeds and juice.
