Yes, there are differences between OSX and Windows in how HTML is handled. Essentially, under Windows, Inquisit embeds Internet Explorer (because it is reliably available on all Windows systems) to render HTML. When run in embedded mode like this, however, Internet Explorer enforces various restrictions that may keep embedded / interactive content such as videos from working. The way a given system is set up and what security settings the user or organization applied to Internet Explorer installations also play a role under some circumstances, i.e. content may work on one system, but not on a different one with different settings / restrictions applied.
I'm afraid there isn't a really good or universal solution here. Ideally, you'd not embed Youtube videos, but instead you'd use standard <video> elements in Inquisit to play the videos. For online use, you can set the <video> elements' /stream attributes to true, that way the won't have to be downloaded in full before the experiment launches, they'll be streamed instead at runtime.