You've already been given so many answers, but here are my two cents:
- Both DU and HSY gets a bit repetitive after a while, but like many have pointed out, DU gives you more ways to change up gameplay. You can live in a dorm, or in an apartment or house, in that world or another, as an YA, adult or elder.
- World-wise I personally prefer Britechester, I think there is more to do, and I love the Oxford-wibe of the city. The great selling point of Copperdale is the Amusement park, but I find it boring and rather dead. You don't see families there, and you can't change anything at the lot.
- BB depends on what you like. I personally like the little bit more rustic old fashioned DU design, while the HSY often feels like it could be better than it is. It's so themed on teenagers that pieces that would work beautifully are ruined by beddings or color swatches that are made to look "teen" (pink and glitter, rainbows, cool designs) and doesn't work for adults. Some of the art deco pieces however are gorgeous. If you, like me, play historical gameplay DU is good for Victorian vibes, and HSY a bit more art deco.
- CAS I definitely prefer DU to HSY, more every day "boring" clothes, which I like.
- I do love the addition of body hair in HSY.
- Aspirations are in my opinion better in HSY than DU, the academic one is really hard to achieve.
- Careers are better in DU than in HSY. Hands down.
- As stated before, right now the clubs in DU are completely unplayable since the last patch, but when they work they are quite nice. You can make your own clubs to make up for it however if you have get together.
- Also DU doesn't work for playing rotationally without cheats, unless you put all your people at the same dorm, then you can play them as a family.
- With either you need mods if you want to be able to choose who your sim goes to school with.
Personally I am glad I have both, even if I only occasionally use the core gameplay of either, I do use the CAS and BB of both extensively and elements of both consistently.
