Answer: Brachychiton populneus, the bottle tree, is native to Australia. It's an evergreen with a moderate growth rate (30'-50' high with a 30' spread), and is often used as a shade tree in low desert areas. It produces clusters of small, bell-shaped, white flowers in May and June, followed by woody fruits. The canopy is dense and will provide the screening and privacy you desire.
Nothofagus, or false beech, is an evergreen tree growing 50'-70' high with shiny, dark green leaces. It does not flower or fruit and the branch pattern is open, admitting filtered light.
Of the two, I'd choose Brachychiton for screening purposes.
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