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Pro Chrome notifications act as a notification drawer
Desktop Notifications uses Chrome notifications to act as a running list of past notification that have not yet been dismissed. This is especially useful if you receive a lot of notifications or you are not at your computer when they are received.
Pro Runs with Chrome open by default
Pro Uses a Chrome or Firefox extension for Mac/PC
Desktop Notifications uses a Chrome or Firefox extension to display notifications. This makes it easy to always have your Android notifications on any computer signed into Chrome.
Con No ability to disable notification mirroring of an application from Chrome
From Chrome it is possible to exit out of a notification but there is no way to permanently dismiss an app from mirroring its notifications.
Con Less information previewed in notifications than other services
Desktop Notifications does not preview the message or provide the email of the sender (only the name). Other services preview the email in the notification.
Con Slight delay
While other services like Pushbullet receive notifications almost immediately. There is a delay of a few seconds with Desktop Notifications. Although the developer is working on it. In response to a user review the developer stated "We had to introduce a delay to the notifications because of the overwhelming amount of users who started using our app recently. Otherwise our servers would melt. :) When you don't receive a notification for some time our app will check less frequently. We don't like this either and are working on it!"