Given that Xbox's consoles have, for the most part, attempted to take Playstation head-on by offering a similar experience, do you think they would be better served by doing things more differently than Sony and seeking to differentiate Xbox, rather than being a direct competitor?

Yes, if they can pull it off well. Personally I have little reason to believe they can though, so in practice my answer is no. Instead, they should capitalize on Sony's shortcomings and use them to gain some momentum and do everything right while Sony is overconfident. I don't think they can do that either, but at least it seems more likely.

Note that I didn't say they can't differentiate themselves from PlayStation. I only said I have little reason to believe they know how to do it well. They could certainly succeed at it, despite how it seems outward.

They tried that with Kinect. Smartglass and to some extent Hololens. Xbox is just not the company to try that stuff.