Synergy = Diversity to cover weakness
Synergy is always a preffered choice in competitive pokemon.
As state, the two are not mutually exclusive. Synergy is actually the step above diversity.
Just having a bunch of random types, just as long as they're all different, is not the way to go. For example, I go with a Fighting type, a Normal type, a Ground type and an Ice type. I am now effectively unable to hit Froslass.
I prefer synergy, even if it's just basic synergy. They may not be the tightest unit, but they have to be able to work with each other, having something to at least cover their weaknesses.
Yup. Diversity kind of goes with synergy. A team needs to be diverse to have good synerygy. A team of all of one type will not have good synergy, and will not be diverse. A team of different types will be diverse, and will have good synergy if the right types are used.