Hey,
Congratulations to getting into both courses. I ended up choosing Oxford which I do not regret at all. However I did also reevaluate the long term plan of doing a U.S. Phd. I think if that is where you want to end up, both of them would be useful, but neither of them will guarantee entry. The Oxford course is a really comprehensive introduction to practical economics but is probably less analytically rigorous (a.k.a math proofs and matrices) than DSE.
Hope this helps.