One was hard, gallus and crime-ridden.

The other was genteel, reserved and safe. Glasgow and Edinburgh have never quite managed to live up to their stereotypes. But, on crime at least, the trends were clear. Until now.

The very latest figures for offending in Scotland's two big cities show figures are starting to match up.

That's because crime is falling in Glasgow but rising in Edinburgh.

If current trends hold for another year, overall offending levels in the two cities will be almost identical.

So what exactly do the numbers tell us? Well, there were 47,000 crimes officially recorded in Glasgow in the last financial year, not including the administrative and less serious ones ranked as mere "offences".

That compares with under 36,000 crimes of the same categories in the capital. But Glasgow is bigger than Edinburgh. So the way to compare would be to look at the crime rate per 10,000 people, the standard international measure.

Now the numbers start to look more similar. The crime rate per 10,000 in Glasgow was 802.5 in 2014-15, down 5.3%. In Edinburgh it was 738.2, up 0.5 per cent.

But these headline figures conceal huge changes since Police Scotland came in to being in April 2013. The crime rate in Edinburgh has risen around 14 per cent under the national recording regime. And it has fallen by 10 per cent in Glasgow. The result: the old stereotypes, always exaggerated, now look hopelessly outdated.

So, to sum up these historic changes, in 2014-15 Glasgow crime was 8.6 per cent higher than Edinburgh's, back in 2012-13 it was 37 per cent higher.

Fariha Thomas, the councillor who chairs local quango Community Safety Glasgow, said: "This is a helpful reminder that, often, crime statistics tell us as much about policing as they do about crime. Unavoidably, they reflect the priority that is given to detecting and preventing particular offences in our communities.

"It would be a mistake to become complacent, but that focus - along with a closer and more effective partnership approach to community safety - is clearly having an impact on crime in the city and, in many ways, our streets are now safer than ever. Over time, that will have a growing positive impact on our city and its image."

Figures for some individual crime categories reveal just how much things are changing from those old images.

Violent crime is falling across the northern hemisphere - although comparable homicide rates show it is falling faster, for example, in Scotland than in England.

Both Glasgow and Edinburgh are less violent than they used to be. But the decline in the west, where the problem was traditionally seen as worst, is steeper than the east.

In the last year of the old Strathclyde Police, 2012-13, the rate for serious violent crime - so called Group 1 offences, such as murder, robbery or serious assault - was 29.6 per 10,000 in Glasgow.

The equivalent in Edinburgh was 20.6 per 10,000. So the Glasgow rate was a shocking 43 per cent higher.

Glasgow now has a violent crime rate of 22.8 per 10,000.

The figure in the capital is 17.2. Glasgow, therefore, is now still shockingly one third more violent than Edinburgh. Knife-carrying - a much reduced crime across most of Scotland - remains firmly a west coast issue. Prevalence was three times higher in Glasgow than Edinburgh.

But all crimes of dishonesty are massively higher in Edinburgh than Glasgow, and that includes robbery, theft with the use or threat of violence. The robbery rate - including street muggings - is 6.4 per 10,000 in the capital but just 4.8 on the banks of the Clyde.

It used to be higher in the west than the east.

Before Police Scotland Glasgow had a slightly higher level of break-ins than Edinburgh. Now levels in the capital - the subject of major controversy - are twice as high as in Glasgow.

So why are overall offending levels in Scotland's two big cities starting to coalesce? Is this a symptom of a national force?

Attitudes, for example, to domestic violence appear to have been subtly different in the old Lothian and Borders force than in Strathclyde, resulting in fewer incidents being recorded as violent crimes.

Or is it that much of the wider campaign against violence, such as the smart tactics against gangs from the Violence Reduction Unit, focused on the most troubled areas of Glasgow?