Helical gears are stronger, they most likely use straight cut gears in racing because there are no thrust forces involved in straight cut gears, and racing uses custom ratios, and straight cut gears are MUCH easier to machine (think about it). Helical gears are used on cars because they are stronger and quieter, more contact time on each tooth, most cheap cars use straight cut gears in reverse (if you stand around in a parking lot, you can hear the winding noise they make) because they are cheaper, no one drives in reverse long enough to complain about the noise.

the reason that broke was probably a combination of that bent shaft and the design of the gear, all of those lightening holes in the ring cause areas for stress concentration (places to break), that and the large distance between mounting holes. Helical gears have side loads due to their design, put a lot of torque against them and they will push to the side pretty hard, throw in another issue like the bent shaft and things can go bad... it probably wouldn't have broken if the gear adapter piece was a full circle instead of a cross.