My first contribution to this thread! I took this last year while in Montreal. Comments are welcome.
The sun seems to be almost directly overhead, so the light is blue and 'unrevealing'. Of the stonework you've included in the pic, only about 5% is in direct sunlight; the rest of the facade is in shadow. The result is that a three-dimensional building looks 'flat' and uninteresting.
Check out the Greek building (post 614) to see what happens when you shoot with side-lighting. The light 'models' the fluted columns, and accentuates the contours on the face of the statue. A nice touch is that the shadowed part of the face is positioned against a lit area of column. Accident? Design? I don't know... but it works.
On your pic, the statue almost disappears into the background. But earlier and later in the day, the sun would be lighting up the facade of the building, and throwing the architectural details into relief, offering the contrast of light and shadow that puts the third dimension back into the composition. The light would also be 'warmer', not blue-tinted.
By walking around a building, you can see how the light changes the way the building looks. From certain angles it will smooth the stonework; from another - acute - angle it may pick up the rough surface texture. Of course, this may take a bit of time, or planning, when you actually don't have time to spare.
The 'trick' may be to emphasise the creativity of the
architect... rather than the creativity of the
photographer...