USA citizen here...

Last fall, I entered Schengen at HEL (from JFK) and departed at VIE (for LHR). At exit control in VIE, the agent was quite agitated when he couldn't find my entry stamp. He had some nasty muttering about those bleeping Finns when he finally found the stamp near the back of my passport, nowhere near any other stamps.

So yes, at least some Schengen border guards care about entry and exit stamps matching.