Mavericks issues with Growly Notes
I'm the developer of Growly Notes. We are are happy to answer questions from users; just choose "Contact GrowlyBird" from the Help menu in Notes.
There is no known issue with people losing data with Mavericks. What does seem to happen a lot when people upgrade their operating systems is that the preferences file gets changed or lost during the upgrade. No one has ever been able to explain why this happens. The preferences file is where Notes remembers which notebooks were open. Almost every person who's ever contacted me about issues like this finds their notes again by either
1) Using File/Open Recent, or
2) Looking in the Notebooks folder inside their Documents folder, which is where the notebooks are stored.
There is one big issue with Mavericks and Growly Notes, however. Apple changed the way that PDFs are displayed in 10.9: they float on top of everything else in the window. So if you put text notes or drawings on top of PDFs, once you upgrade to 10.9 they will display beneath the PDF instead of on top of it. There is no workaround: you have to slide the PDF out of the way to see the other notes.
I'm working on an update that will contain a fix for this issue (among many other things). But it may be a while, at least a month, before it's ready. If putting notes over PDFs is something you do a lot, I suggest waiting for the next update to Notes before you switch to Mavericks. Otherwise it should be safe.