120v circuits draw their total amperage from one hot leg. It's not at all uncommon to have a 120v circuit that's really not to par due to having long runs of wire, multiple junctions, small gauge wire, bad quality wire, bad connections, or that's simply overtaxed from multiple appliances running of it, along with several other potential ills....many of us face this issues in our shops without even knowing it. Plugging a typical 1.5hp 15 amp contractor saw to that circuit can result in the saw not really running at it's full potential, creating excess heat due to the voltage loss, slower startups, slower recovery from lugging, excess heat, shorter motor life, etc. (15 amp nominal amp draw, 50+ amps momentary peak amperage all coming through that single hot leg). That performance would seem normal if it's all we've ever been exposed to. Switching that same saw to a 240v (aka 220v) circuit will usually cure the ills caused by the sub-par 120v circuit....you'd get faster startups, faster recovery from lugging, etc., giving the impression that the saw is now more powerful. What's really happening is that the saw is finally running to it's full potential. Installing a proper 120v circuit would likely cure the same ills, but it usually makes more sense to install 220v if you're going to install a new circuit. 220v circuits split their amperage draw across two hot leads....Half the amperage running across two hot leads is far less likely to ever reach the point where the supply circuit will experience notable voltage loss issues from the demands of that 1.5hp 15 amp motor. It also allows you to run larger motors that have a higher amp draw.
To me, it's really not an issue of which way the windings of a given motor are wired (parallel or series), but how well a given circuit can supply those windings.