Music theory gives us a language to communicate about music. Partimento and Schemata add new words to that language.
All theory changes the way you listen to music. Learning about major and minor tonalities, modulations, form, or Augmented 6th chords allows you to hear music differently. In fact, almost all music theory seeks to categorise music in a way which allows people to communicate about it. Imagine trying to communicate about football without talking about player positions, formations, or rules.
Partimento and Schemata both focus on learning music at the level of the phrase. Partimento teaches common phrases such as the Rule of the Octave and certain sequences. Schemata trains the musician in hearing, analysing, and playing music at the middleground (skeletal phrase structure) rather than foreground (diminution). This allows the listener to hear music at the level of the phrase (particularly the counterpoint) rather than simply the surface notes.
Further to this, Partimento and Schemata teaches common phrases in common-practice music. This allows the listener to hear when a composer is doing something which is conventional, or unconventional.