Most of the previous comments get at the main issues.
The main differences are:
1) They feel different in your hands so, personal preference: whichever feels better in a person's hand is the one he/she will prefer. The different handles do not noticeably change speed, dwell time or feeling from the blade, so it really boils down to personal preference and there are advantages and disadvantages to both.
2) Straight is better for twiddling so a lot of LP defenders use straight.
3) With flared you can have a very relaxed grip and hold primarily with index finger and thumb and keep the other three fingers loose. This gives you more whipping action and so, more racket acceleration and spin because of the whip mechanics of the stroke. The reason is the thinner neck of the handle with the thicker butt of the handle. However, a guy like Timo Boll, who uses a straight handle, still gets great acceleration and spin on his strokes. So, technique will always win out.
4) The shape of the flared handle should actually enable you to use more wrist on shots and serve. The thinner neck is less in the way of the movement of the wrist. The thicker butt of the handle actually helps you use the wrist more because of how you can press the heel of the hand into the butt and get extra movement from the head of the blade because the neck of the blade is not in the way.
5) Based on the information above: because you are encouraged to grip a little more firmly with straight handle, it is thought to make the FH a little more powerful. Because of the ability to generate more whip and use more wrist, flared handle is thought to be a little better for BH and serves.
The last thing I will say is that, if you look at the top pros in the world and then you look at the ones that are offensive players, over 95% of them use a flared handle.
It is worth contemplating why if you play a two winged offensive looping game.