Leaning one's body to go fast in a turn (say one is racing on an on road track) is for traction, not for the turn. By leaning over (hanging off the bike as one can see roadracers do), one allows the bike to be a bit more upright (to maintain the tire's footprint, read increased traction) than one that does not hang off the bike.
Shifting your weight over to turn is actually counter-productive as the bike counters that motion (Newton's Third Law of Motion, Action and Reaction) as the rider is a counter weight to the bike in those circumstances. Racers turn fast by a snap counter steering into a turn that forces the center of gravity to shift and snap the bike into a lean. The racers are hanging off the bike for the traction they need in a turn to maintain traction of the tires, not for the turning.
For cruising, the bike with the lower center of gravity should be more stable as one doesn't have to hang off the bike in turns at non-race speeds.
BTW, one needs to counter the gyro-scopic effect of the wheels/tires, not the motor.