The workload at Oxford is huge…but there is definitely time for ECs 
But…your post says you already know what you want, and are only anxious about whether you are giving something up to get it. Fact: you are. Other fact: you will be giving something up if you choose the other way. That’s the nature of choice! Especially when you have two great choices.
If you won’t have to take on any debt for either of them, follow your heart. What you do in college will matter more than anything.