Will a bed built with oak be better than a bed built with another kind of wood ?
The quality isn't directly related to the type of wood. The quality depends solely on the skills of your carpenter.
However, certain dwarves prefer one kind of wood over another, and having a bed with their favourite type of wood in their bedroom will give them happy thoughts.
This goes for anything though, a statue of their favourite type of rock will also give happy thoughts if it's in the dining room.
Additionally, wooden beds made of nethercap wood will inherit the fixed temperature of the log, which makes the bed magma-safe. Nethercap can also be used to build wooden magma-safe pumps or doors or what have you, which can occasionally be useful.