Both are important but poor design in any of the upstream activities are generally more difficult to correct. Changes to the functional specs for example will naturally generate a lot more work then some verbiage changes on the interface.
Any meaningful changes to the database generally require coding changes as well, so I personally spend a lot more time agonizing over database design decisions then coding decisions (although I'm sure I'm not the only one who has spent an hour or two trying to find the perfect name for a class).
