Sentry Ward and Dust of Appearance - General rule to use

 

Sentry Ward

Sentry Ward for protecting against invisibility heroes. About to pushing / teamfight / rosh and want to see whether Nyx Assassin is lurking nearby, drop a Sentry Ward. While it provides vision for a lot longer, it is less suitable for killing since you will lose vision of they pass out of its truesight range.

Dust of Appearance

Dust of Appearance for killing invisibility heroes after they have revealed themselves/ preventing them from go invisibility if you are trying to gank. The Dust debuff will stay on them if they leave ranges, and also slow. Since they have to be there when you drop it however, you generally do not use it unless you are already pretty sure someone is invisibility nearby. Note that if they have a Diffusal Blade, the Dust can be purged.

When you are fighting against perma invisibility heroes, you need both Sentries and Dust at all times

Honestly, when you are fighting against perma invisibility heroes, you need both Sentries and Dust at all times. For certain heroes, one is ok (like Sentry Ward vs Templar Assassin). If you are laning and you have one or two stuns, a Sentry Ward is ok vs Nyx Assassin or Bounty Hunter. But in late game, you needs both Sentries and Dust. When you are pushing or roshing, I would prioritize Sentry Ward over Dust of Appearance. You need to know where the invisibility heroes are so they can not initiate on you. There is no point in having Dust of Appearance really if the invisibility hero initiates on you and wins the team fight. Also, when an invisibility roamer roams into your Sentry Ward, you can Dust of Appearance and kill them. Otherwise you won't know to Dust of Appearance. Later in the game against perma invisibility or even Mirana invisibility, you want to get a Gem of True Sight to replace the use of Sentry Wards

Defending

When defending, I would prioritize Dust of Appearance over Sentry Ward if you have tower vision (and depending on what tower), because probably the invisibility heroes isn't going to initiate if you stay within tower true sight range, they're going to come in after the fight.

Dust of Appearance is more offensive, like for chasing down Nyx Assassin, Riki,  Bounty Hunter or Shadow Blade. Sentry Ward are better when you are getting ready to fight defensively and you know where the fight will be - drop a Sentry Ward or two and you will see that invisible initatior run in, and then you can destroy them.