First, let’s note that all of the hub models, including the ADT model, have exactly the same basic home automation capabilities. There are a few differences, like not all the devices work with the V1 hub, the V2 hub has some local video features which were dropped for the later models, the V3 hub can connect by Wi-Fi as well as Internet and also supports the zigbee 3.0 standard , etc. but as far as the basic sensor gets tripped, light comes on, they’re all the same.
What the ADT model adds are some very significant security features which are not available on any other SmartThings hub models.
At the present time, the only smartthings hub model which is really appropriate for security is the ADT model. That’s why all of the links on the smartthings website which take you to security will take you to that model.
There are a couple of basic reasons for that.
1) More reliable sensors. The ADT/Smartthings dual logo Sensors use a completely different network protocol than any of the others that work with SmartThings. It’s not zwave, it’s not zigbee. It’s a point to point Topology instead of mesh. It should definitely result in fewer false alarms and potentially fewer missed alerts.
2) The ability to arm/disarm even if the Internet or the smart things cloud are not available. If you have your system in “armed” status, All of the other hub models store that information in the cloud. So if the Internet goes out before you get home, unless you are using the ADT model, you will have no way at all to disarm the system and keep your sirens, etc, From going off when you go in the house. Lots of threads in the forum about how annoying this can be.
Since the mobile app won’t work either if you can’t reach the smartthings cloud (Communications go from your phone to the cloud to the hub, not from your phone to the hub directly even if they are on the same Wi-Fi), you will have to individually go around the house and take each siren off power.
And your alarm system will continue to re-alert every time you open the door or trigger one of the other sensors. It can be very annoying.
In the same way, if you normally arm your alarm system when you go to bed, and the internet goes out before then, with the non-ADT models you will have no way to arm the system. It will stay disarmed until connection to the smartthings cloud is restored. 
In contrast, the ADT model can be armed or disarmed even when the Internet is out by using either the panel or the key fob.
3) Notifications. All notifications from the non ADT models, even to your own phone on the same Wi-Fi, Are sent from the smartthings cloud, not directly from the hub. Which means no cloud, no notifications. No Internet, no notifications.
In contrast, the ADT model has its own cellular module so it can communicate directly to the professional monitoring service. (To be honest, I’m just not sure if that function is available if you are self monitoring with that model or not.)
4) Performance in a power outage. Most non-ADT hub models do not have a battery backup. The V2 hub does have that option, but there have been problems with battery leakage over time, so a lot of people don’t use batteries with it anyway.
In contrast, the ADT hub model has a good battery backup.
So even if your power goes out, the ADT model hub can continue to send notifications to the central monitoring station. The other models cannot.
5) Fire Dispatch. The Scout monitoring service can only do “intrusion alerts,” which means they can only call police. They cannot call the fire dispatch directly. This can cause delays because a police car has to come out first. It also means you may not get the same insurance company discount if one is available on your policy.
In contrast, ADT is authorized to report a smoke alarm directly to fire dispatch in most jurisdictions as well as make a general 911 report. That can literally be life-saving.
I’m not 100% sure on the following, but it looks like The unofficial Noonlight option also just makes a general 911 call for you, like someone walking past your house who hears a siren. They do not appear to be authorized to call fire dispatch directly. So that would be the same two-step process: first a police car would come to investigate, then they would call the fire department if appropriate even if it were a smoke alarm which triggered the initial call to the monitoring center.
6) Tamper alert If you are using the professional monitoring service, the ADT model hub has a tamper alert which is treated the same as an intrusion alert. The other model hubs do not have this feature.
7) Visual Interface. The ADT model hub has the status panel design which is very different from any of the other hubs. It’s specifically designed to make it visually obvious to someone, even a child or a guest, how to arm or disarm the system.
You could create something similar for the other models but you would have to Buy an additional device and maybe additional software.
This one may not be as big an issue for many people as the previous features, but it’s just another obvious example of how the ADT model was designed from the beginning to be a security system.
8) The ADT model has a built-in siren. The other hubs do not. Again, you can buy an additional device and add a siren easily to the other hubs, but this one has the advantage of being able to be armed and disarmed even when the power or the Internet are out.
I’m sure there are other security features that the ADT model has that the other ones don’t, these are just the major ones that I think most clearly show the differences between a system which was designed from The beginning to be a security system and a cloud-based system which was not. 
Note also that at the present time all custom code runs in the cloud. That means that all the clever community-created solutions you will see in the forum That people created before the ADT model was released to add more security functions to the other hubs still require that your Internet is working or they won’t work at all. That may be OK with you, but it’s an important fact to be aware of.
