I would love to see a discussion of this.
When designing things like garden gates and arbors, even fence panels and window
placement I often create stuff that doesn't look quite right, other times it
looks great.

I understand to concept sorta, of the golden rectangle but what about other
shapes like rounded top gates, ovals, etc.

Examples.
I make one gate it looks great another looks a little off, but I really can't
see why.
I make a lattice frame arbor and it looks terrific, change the size and shape of
the 'holes' or the boards and it looks awkward, clunky.