I was one of two or three lefties at the UEA cricket club, out of nearly 40 players, which would reflect the actual percentage of left-handed people better than at most clubs (and I'm not really left-handed). I used to come in for stick from my mates for having an advantage. The argument was that if the bowler is right-handed and slanting the ball across you, which he has to do, then you get far more balls to hit to off, because of the natural width given if the bowler only makes a slight mistake with his line. The same applies to the leg-side, with more balls being given to hit. This is true, but only up to a point. Personally I find it hard to face a right-arm outswing bowler (to me), who swings the ball from outside or on leg stump towards middle and off, because I see the line early and get ready to play into the leg side. I also think that off-spin is harder to play as a leftie, if the bowler is good enough to consistently pitch on the off-stump and move it away. But that may be my own flaws as a batsman.
The discussion would then move on to the LBW law, and I certainly think lefties have an advantage here. I think the solution is for bowlers to practise bowling around the wicket more, thus replicating as best they can the line they'd bowl to a right-hander. But few bowlers are willing to do this. The vast majority of the times a bowler decides to come around the wicket to me, his first ball will be going down leg, giving easy runs, though of course there are exceptions.
Listening to some right-handers talk you'd think there was a massive conspiracy by left-handed batsmen to take over the game of cricket! Of course, this is completely true.