Is a 1080i video more prone to pixelation when compressed than a 1080p one?

I’m going to guess it has as much to do with the presentation app.
Streaming sites rely on software (e.g. silverlight) that makes a point of smoothing out missing data and motion.
Blu-Ray movies are totally engineered and produced for quality viewing in all respects so you’re unlikely to see dropouts or missing bits unless they intended that.

For whatever reason the presentation on cable channels does not necessarily do that, especially live programming. Sometimes it’s the cameras (especially for fast-motion artifacts), sometimes it’s the transmission uplinks….