The use of mobile phones while driving is a very common phenomenon that has become one of the main causes of traffic accidents. Many studies on the effects of mobile phone use on accident risk have focused on conversation and texting; however, few studies have directly compared the impacts of speech-based texting and handheld texting on accident risk, especially during sudden braking events. This study aims to statistically model and quantify the effects of potential factors on accident risk associated with a sudden braking event in terms of the driving behavior characteristics of young drivers, the behavior of the lead vehicle (LV), and mobile phone distraction tasks (i.e., both speech-based and handheld texting). For this purpose, a total of fifty-five licensed young drivers completed a driving simulator experiment in a Chinese urban road environment under five driving conditions: baseline (no phone use), simple speech-based texting, complex speech-based texting, simple handheld texting, and complex handheld texting. Generalized linear mixed models were developed for the brake reaction time and rear-end accident probability during the sudden braking events. The results showed that handheld texting tasks led to a delayed response to the sudden braking events as compared to the baseline. However, speech-based texting tasks did not slow down the response. Moreover, drivers responded faster when the initial time headway was shorter, when the initial speed was higher, or when the LV deceleration rate was greater. The rear-end accident probability respectively increased by 2.41 and 2.77 times in the presence of simple and complex handheld texting while driving. Surprisingly, the effects of speech-based texting tasks were not significant, but the accident risk increased if drivers drove the vehicle with a shorter initial time headway or a higher LV deceleration rate. In summary, these findings suggest that the effects of mobile phone distraction tasks, driving behavior characteristics, and the behavior of the LV should be taken into consideration when developing algorithms for forward collision warning systems.