The phone app for Notezilla is created using Xamarin Forms. I like the way Xamarin Forms has grown. It works pretty well.
If you are looking for SQlite .Net PCL library, you might find multiple. But I will tell you which one is good.
For last few years I had used Sqlite.Net PCL and Sqlite-Net Extensions in my app. While I was debugging performance issue in the iOS version of my app, I found that the performance lag was due to a single linq query. It used to take 7 seconds. Xamarin Forms list view which listed our records was performing too slow. This was the case only in iOS. Not in Android.
So I looked for an alternative. And finally found the original Sqlite-Net-PCL project that is being maintained till date. I implemented Sqlite-Net-PCL and found that the same linq query executed in less than 1 second. This was a great deal for me.