Most left-handed hitters in the majors aren’t truly left-handed. They are naturally right-handed and learned to bat left-handed. From 2002 to 2013 only 43% of all left-handed plate appearances were from left handed throwers.
I thought the there may be a somewhat different batted ball profiles for the two groups such as right-handed throwers are more fly-ball prone. After totaling the values from 2002 to 2013, the results are almost identical:
And here is the percentage mix for hits:
The only possible differences would be in FB% and K% being higher for right-handed throwers.