Actually, in two Vasco Rossi songs — 'E già' (he uses 'sono ancora qua'), and 'Vieni Qui', and other examples, qua seems more static and qui appears to involve more movement. However, my Italian friend suggested that they're more or less now interchangeable. She thinks there's a fair bit of laziness creeping into the language though
The pair are often interchangable but consider thinking this right here, somewhere near here vs that just over there or that place very far from me: qui is more localised & specific close to the speaker like "my house"; qua covers a wider & more general area like a city or country. Similarly lì is more localised or exact but still far away; là is far from the speaker but more approximate. Exceptions 'quello là' is specific but just not as near as 'questo qua'. When speaking don't agonise, just say one or other and still be understood.