VidYard provides pretty limited bandwidth considering they promote "Force HD". And masking RTMP as "Instant-Start Technology" is a little sketchy, IMO. RTMP isn't rare. BOTR's API is pretty much perfect and having the free add-on ad network service is pure brilliance.
I'm not sure I understand the "limited bandwidth" comment either. As it states on the VidYard pricing page, VidYard offers bandwidth well into the terabytes with no mentioned limit. Additionally the pricing for this bandwidth is quite literally 10x less than BOTR.
Instant start technology is very different from RTMP. RTMP is just one of VidYard's many streaming protocols and is unrelated to the technology required to play videos instantaneously.
For a direct comparison of VidYard vs Vimeo, scroll to the bottom of the vidyard homepage