The frame rate when watching the live view (over WiFi) on my phone doesn't seem as smooth as when I watch them later on my computer, what gives?

This is normal. The frame rate output over WiFi is reduced somewhat from the full HD for several reasons. For one, this is done in order to work with a variety of phone types, not all of which are able to render HD video at full frame rate. Another reason is that while the BlackVue is streaming the stored video to your phone, it's also still recording video at the same time. Rather than compromise the recording quality of the current video by the demands of also transmitting/displaying full HD video, the transmitted video is just sent out at slightly lower quality. Full resolution is always still available of course by copying the video to your computer.