We have a pretty good idea of what it would look like since most of the western countries (esp Europe and Canada) are already basically secular. What few practicing Christians exist in these countries are mostly borderline secularists who are not really serious about their faith.
What I see in the west is a society that is increasingly selfish, materialistic, sexually immoral, and full of spoiled and childish adults who only grew up thinking about what society owes them and not about giving anything back or making any kind of meaningful self-sacrifice for their country, for their family or for God. What you end up with is a society that has a fatally low fertility rate (in most western countries it is well below 1.8) that will very quickly result in economic catastrophe leading to a complete collapse of society, if not corrected.
Jesus teaches us the importance of loving ones neighbour as oneself above all other commandments and without God at the centre of this belief it will inevitably get distorted into something really ugly: this is why we now see society justifying the murder of unborn children and the elderly as being some twisted act of compassion. If God exists, which I know He does, then a world without religion would be a blind world that is heading off a cliff with no direction or way of correcting course.
