This work studies the timeliness of the stalest stream (TSS) for the multi-stream vehicle-to-infrastructure status updating link in vehicular networks. Specifically, this work explores whether the asynchronous (ASY) or synchronous (SYN) updating pattern is better, and studies the TSS difference. A typical two-stream scenario is considered, where two vehicles separately update status data to a roadside unit. The age of the stalest information (AoSI) is adopted to evaluate the TSS. By analysing the distribution of the per-steam age of information, analytical expressions of the time-average AoSIs under the different patterns are derived. Based on the time-average AoSI, it is found that: The SYN pattern always outperforms the ASY pattern in terms of the TSS; The TSS difference becomes greater with the improvement of the channel conditions; The maximum time-average AoSI difference is a quarter of the update transmission time. Numerical results indicate that: The TSS becomes worse with the increase of the asynchronization level; The TSS can be improved significantly through enhancing the updating synchronization, particularly when the channel conditions are favorable.