In most cities the answer is simply south. In Calgary it is a trade-off, and the reason is your driveway in February.
A south-facing backyard means a north-facing front. In Calgary that matters more than it does almost anywhere else, because a north-facing driveway and front walk sit in shade all winter. Snow that melts off a south-facing driveway by noon can stay on a north-facing one until spring, refreezing every night into a sheet of ice you are chipping at in March.
So the honest answer is that both orientations have a real cost, and which one you should want depends on whether you spend more of your life in the backyard or on the driveway.
If you ask Calgarians who have lived through several winters, a surprising number will tell you they would take the south-facing front for the driveway. That answer almost never appears in listing copy.
South and west backyards are the ones most often advertised, so they appeal to a slightly wider pool of buyers. But the effect is modest and easily outweighed by everything else about a home — nobody sensible buys the wrong house for the orientation.
Where it genuinely matters is at the margin between two similar homes. If you are choosing between two comparable houses on the same street at a similar price, the orientation is a legitimate tiebreaker, and the driveway is worth weighing as heavily as the deck.
Do not rely on the listing. Stand in the backyard and look at where the sun is, note the time, and look at the front for how much shade the house throws across the driveway. In winter, look at what the snow on the driveway is actually doing compared with the neighbours' — it tells you everything.