You can use your WP membership with Delta as well. You will earn miles on DL, so I don't see why you would want to switch. The only time the switch makes sense is when you are elite and have a lot of DL flights in the future (a LOT more than NW) and you want to get the Elite perks on DL (like upgrades), but the status match is debateable.

Anyway, I say if you just have a DL flight out of DTW - stick with WP. (AA is a different story, but for 5K, it's not worth the hassle.)