I have the sydney sleeper in my inventory in TF2. Looking at the stats:
+25% charge rate
On Scoped Hit: Jarate target for 2 to 8 seconds based on amount charged
Headshots or fully charged shots cause an explosion of Jarate.No random critical hits
No headshots
These seem pretty bad, because one of the main attractions of the sniper class in general is triple damage headshots. What good is this weapon, if I can't headshot? Why would I want to use it?
It's a viable sidegrade.
It makes sniping more reliable (no need to headshot) and gives you a more supportive role.
The jarate effect is especially useful by making enemies retreat and scaring them away.
Extra charge speed is there for help the sniper do some basic picking, 150 bodyshot can easily take out medics and scouts.
You can extinguish teammates by shooting them.
Headshotting and the explosion of jarate is nice for pushes (like enemies on the cart or going through a choke), it will coat all of the enemies.
It's great against DR spies, since marks them when they feign death. Additionally, you can apply jarate to ubered enemies!
They won't take damage during the uber obviously, but the jarate will probably finish them off once the uber fades (for best results, apply near end of uber). The pocket probably won't even notice that his buddy is covered in jarate. Do note that applying jarate to the pocket won't last very long, due to the healing.
Finally, if you're worried about enemy snipers (because their stock can kill you in a quickscope headshot, use the danger shield.
Also, many of the guides on the internet are outdated, it has since been updated to apply jarate on unscoped shots and explosions on headshots. (thanks to Robotnik for reminding me of this)
Taken from an answer I wrote on reddit a long time ago, link here.
Personally I never see a real reason to use the sleeper as a sniper, the points that Riker suggested are all well and good but a lot of them can be countered for the most part by using stock or though game sense.
For example, if I see that a medic has an uber then I would much rather kill him as quickly as possible with a headshot/scare him into an early pop and lose some of the effectiveness that the uber could have had. With DR spies, after some time you generally get a feeling whether or not a spy has taken enough damage to have actually died and also the DR uncloak is rather loud so you can usually hear it. The danger shield is usually a simple downgrade from the stock SMG unless you are being heavily counter-sniped, as you can lose a lot of close range damage if you are not as good at hitting closer targets while scoped.
For countering pushes to me it seems more like personal preference, since the jarate explosion definitely makes the enemy push easier to kill but I also find that they are a lot less eager to stick around when their medic has a hole the size of Ohio in his forehead. Heavies also become much harder to deal with (from 450HP) because you can no longer get a quick kill, I believe it would take 3 full charge shots with a sleeper (I probably have that wrong, I'm not sure what the damage% increase is). This preference may be because of the fact that I prefer to play more competitive style formats rather than casual but I've never really observed a time where the sleeper is more viable than the stock.
