Not an upgrade nor a downgrade. Two different approaches. Both could be described as "bright with balanced mics and well extended bass" but that's all they really have in common.
The Shures are tracking/monitor headphones that tend to bring out grain and have very clean, solid bass. The Beyerdynamics are a staple for hi-fi listeners who prefer a balanced sound signature.
I've owned both and only ended up re-buying the 840s. That entire Beyer series (770/880/990) just sounds a tad too smooth and slippery for me. Although the bass quantity differs in each version, the same wide/smooth bass style is always evident and I couldn't come to enjoy it.
Then there's the word "transparency", which nobody seems to use the same way. The DT 880s sound more transparent in the sense that they sound more like live music-- smoother --, but the Shures sound more transparent in the sense that one can focus on recording artifacts with less difficulty -- more bite --. Again, evident of the latter being more of a studio monitor than a leather armchair hi-fi set.