After becoming a dad and travelling with kids, I'd choose NONSTOP if premium is reasonable too. And evening/red-eye flights too, please
Either way, I'd only want to connect if the transit airports are interesting enough, good lounges (e.g. IST *A lounge), or long layover to do a quick day trip (ZRH or ICN), or lastly - price errors!! (Wideroe LGA-YUL-ZRH-MXP is brutal with 2 kids, but for $250/person!!)