The old app does not depend on Cortana and Windows Ink, which also makes it useful for privacy-conscious people. The notes themselves are also a bit smaller, so users like their compact appearance more. The performance difference is especially visible on less powerful hardware like Atom and Celeron CPUs. It starts immediately and works much faster.
It consumes notably less system resources. Many prefer the good old classic Sticky Notes app.
However, a lot of users are not happy with this new change. Starting in version 3.0, the modern Sticky Notes app includes a dark theme, the ability to sync notes between your devices, and tons of other new features. You can create check lists and use it with Windows Ink. You can type a phone number and have it recognize it, and recognize URLs too which you can open in Edge. For example, the new app lets you create Cortana reminders from your notes.
The new Sticky Notes app is a Universal (UWP) app, which comes with different features but as is Microsoft's way of doing things, it doesn't include all the features of the classic app. Now, its place is taken by a new app with the same name. With Windows 10 Anniversary Update, Microsoft discontinued the classic Desktop app 'Sticky Notes'.
