Pretty much agree with tohu for daily usage. The different usage & connotation is imo mainly evident in science & industry. Would explain the weird ngrams chart imo.
On the google trends graph you can see clearly the peak when Fukushima happened around march 2011.
Überprüfung has the connotation of a independent 3rd person/institution checking a system while a
Prüfung is e.g. a school or phd test inside a institution. The blue google trends line oscillates pretty periodically, at the end of every year there are no
Prüfungen, mostly in the middle.
The rise of
überprüfen in ngrams is imo linked to the continuous arising of technological systems in the last century and more & more
Überprüfungen in our technological society. Here the connotation and meaning of
Überprüfung is imo known and clear, esp. in industry/science.
In science you also say
gegenprüfen, when several scientist/groups independently check the same hypothesis/theory.
Ich prüfe meine Daten/Behauptung vs.
Ich überprüfe eine fremde Conclusio/Messdaten. The prefixes
gegen/über dont say anything about quality or number of tests, but what it refers to.
über simply implies/connotes someone over or outside of the hierarchy of the proved institution/system is checking. In English this distinction doesnt seem to exist according to ger/eng dictionaries.
Your XML-Parser is basically an exterior softare checking your code, so you would say
überprüfen. If you "parse" your source code yourself by looking over it and check spelling,
prüfen would imo be more correct. But here its really überhairsplitting :)