Unlike Zurich - a business focused city, Basel it's a much cultural one, in my opinion (because it's home to FC Basel, doh! just kidding).
Home of some world-renowned architects' work, it's no big deal there to walk randomly on streets and find a building that wears the signature of Mario Botta or Hertzog & De Meuron and Johann Jacob Stehlin.
There are lots of great museums like The Museum of Fine Arts, Schaulager Museum, Tinguely Museum and The Museum of Swiss Architecture, from which I enjoyed most Schaulager - it hosted an exhibition dedicated to the lifetime work of artist Paul Kahn (google it, it's worth it), I wasn't allowed to take any photos, but the ideas behind every piece were fantastic ( for example there were some portraits of communist-nazist-fascist liders such as Lennin, Stalin, Hitler, Mussolini, hanging high from the wall upside down- so in order to see them you needed to bend down in a position from which you were showing you derriere to them without even realizing what you just did - one of a 30 person group was smarter and pointed that out...big Aaaaah *lightbulb over head turning on* moment)
The nightlife seems to be a lot more present than in Zurich (maybe because of the football related thing - and the locel people seemed younger), and the restaurants/shops in the center ar open untill late in the night,but the prices are still spicy - some greasy chinese food I get in Bucharest for 5 euros a ton, here was around 35-40 euros and their traditional food - fondue ( melted cheese that you eat by dipping a piece a bread on a stick in it)- a very modest quantity that was supposed to feed 4 costed 60 euros.
Anyhow, I loved Basel beacuse I loved Zurich - they are very similar cities:
Lake -✓
Mountains -✓
River -✓
Boats -✓
Bridges -✓
Gothic catherdals near the lake -✓
Stone buildings -✓
Houses with flowers and shutters at the window -✓
Expensive prices -✓
Lots of parks -✓
Fancy people -✓
Great architecture -✓