It's a combination of both. For example, it's not like fantasy sports where you have to win specific categories, so you won't have to worry about holds, but while ERA/WHIP/K:BB would be important for a bullpen, it wouldn't be a wise strategy to build your bullpen entirely out of closers. First off, that would likely run you dry in salary, but most closers want to be closers and nothing else, so you'd have a tough time getting a lot of those closers to "accept" bullpen roles.
That said, it'd be wise to delegate your setup/middle relief roles to actual setup and middle relief players. Putting a closer at middle relief may be tantamount to putting a catcher in the outfield.