Technically, an XML file is an ASCII file - it's just an ASCII file with a specific format. That said, it sort of depends on the information you're saving as well as how you intend to access that information.
If you do not want the configuration information to be human-readable or human-editable with a simple text editor, then you will want to either have a binary file or keep using the flatten to string which gives you a string looking like gibberish.
The XML format is a good format, but you will need to decide on a document structure. If you use LabVIEW's built-in functions that flatten data to XML, you're pretty much stuck with the format they provide, since if you change the format you will likely not be able to read it using LabVIEW's built-in functions. If you use your own structure then you will need to use XML functions to read the document using the DOM.
LabXML is one possibility, and I've used it for a number of years. The caveat is that it's Windows-specific. It also hasn't been updated in a while. One warning: If your XML file is large, reading and parsing can take a while.
The INI format is also another popular format. It's fairly standard, but it is limited due to its simplistic structure. The advantages are that LabVIEW has built-in functions to read/write INI files, and while they are bloated, they work. If you're looking to store information from clusters, strings, etc, you should take a look at
OpenG's functions which provide functions for reading/writing clusters to INI files.