There is no definitive answer to this question as it will largely depend on the specific bike helmet that a rider chooses, and how it is used. However, many experts believe that more expensive helmets do offer better protection against head injuries in general. Specifically, those made from heavier materials are typically thought to be more durable and resistant to impact forces than cheaper options. Additionally, some high-end designs may also feature additional safety features such as airbags or ballistic reductions which could further increase their protective value.