Both methods $broadcast and $dispatch are now merged in the $emit method with the same syntax as the old version. Unfortunately, replacing every instance of $broadcast and $dispatch with $emit is not guaranteed to always work because the pattern used to manage events is a little different now.
In Vue 1, you had events follow a path either downward (for $broadcast) or upward (for $dispatch), and horizontally (for $emit) through the hierarchical tree.
To be honest, I never liked having two (three if you count the old $emit) methods for emitting events. It was confusing even in the smallest contexts because you had to ask yourself is this event for parents or children? Most of the time ...