I have the View but couldn't find any Facebook videos to try. But to fix the default app issue, go to Settings > Applications > Manage applications. Find the app you want to fix and select it. Scroll down to the section labeled "Launch by default" and then hit the button "Clear defaults". Next time it should ask you what you want to open with.To be clear, this done to the app that is the default to be opened with. In this case it would be the browser. There is a market app called ClearDefault that will clear all default launch settings at once for all apps.
Ok, I found where someone linked to a YouTube video in a post. When I play the video, it goes black but plays the audio like you said. Looks like it's a problem with the Facebook app itself. On my EVO 4G phone clicking on the thumbnail for the video it takes me right to the YouTube page. Both have the same version of Facebook, v 1.8.1.
Clicking on the link to the right of the video thumbnail takes you right to the YouTube page. I don't think you can change that. On the YouTube page, the video works fine on either device.