Kennedy Town has a lot more randomness (or diversity) to it.
Went to Ap Lei Chau the other day for a hair cut and the only option in the $60 range was "1". Kennedy Town has more. Want a quick take away? Kennedy Town has more options. Craving some regular vietnamese food? Kennedy Town has more options. Looking for a random widget Kennedy Town has more shops. Want to go to a gym? Kennedy Town has more options and as far as I know, Ap Lei Chau folks have to get to Wong Chuk Hang.
KT also has a pretty decent LCSD center for swimming and sports - Ap Lei Chau, well you'd have to get on a bus or the MTR.
KT has a slightly younger feel to it - given that it has become home to many younger / single expats and has a sizable HKU grad population living there.
Make a list of random things that you would do without having to plan a commute or use public transport... look for them in both locations and you'll find that KT has more options.
If you're looking at a rental and the cost difference is negligible, I'd go to KT.