The aggressiveness of the batsman's stance will mostly depend on the abilities of the batsman and the bowler. When facing a faster bowler, a batsman will often adopt a defensive stance designed to keep himself between the ball and the wickets, either blocking the ball or driving it into the ground to avoid being caught out. When taking a shot in a defensive stance, you will transfer your weight to the rear foot during your swing, allowing you more reaction time as the ball comes in.
A more aggressive stance is adopted when a batsman has more confidence against a specific bowler, or when the team needs some runs. Much like baseball, turn your body out slightly toward the bowler. Don't turn out as far as baseball, however. The baseball swing is horizontal to the ground, covering more area, whereas a cricket swing is vertical. Instead of driving the ball into the ground, the object is to put more force into your swing and direct the ball to a certain location on the playing field.