We have the same problem in Canada with some differences. Automatic assault rifles are generally not used often. Don't know if we are limiting them more than US or not. Some examples of mass shootings in Canada:

1. Shooter went into a French Canadian University and shot only females (less than 30 I think).
2. Shooter shot unarmed serviceman at a Memorial in Ottawa and then crossed the street and
entered the parliament buildings. He got in a struggle and shot the guard in the foot. Shooter
walked by 2 meeting rooms that currently had the complete cabinet for the Conservatives and Liberals.
If had he entered those rooms with a R15 we would have lost 90% of the government (ruling and opposition).
He had a long rifle with 3 bullet clip. The sergeant-at-arms and his security staff ran after him with pistols and
caught up to him and killed him in a hail of bullets.
3. Shooter got access to Quebec government buildings and caught most of the representatives,
all sitting down in the legislature. ...like fish in a barrel ... luckily, the sergeant-at-arms talked to the shooter and was able to calm him down
and give up his weapon. He had a hunting rifle I think.

NOTE:
The formal role of a sergeant-at-arms in modern legislative bodies is to keep order during meetings, and, if necessary, forcibly remove any members or guests who are overly rowdy or disruptive. A sergeant-at-arms may thus be a retired soldier, police officer, or other official with experience in security.

So I can't say we are better, maybe just luckier so far.

I have noticed that the shooters generally only have the stomach for shooting for a short period of time. Perhaps they regret what
they done soon after starting. If the cops can get there in less than 3 mins maybe most can be saved. Perhaps we should look at negotiation, understanding and try to limit how many bullets/sec a shooter can shoot.
They don't wake up one day and decide to kill. They seem to be reaching out for quite some time before bad things happen.
Identify problem people now and get them some help. Look at people around you and engage with some of the misfortune people suffering
metal illness.