Yes and no. What is bid on is your monthly schedule. Those can be well built, or pretty crummy. For instance, one schedule might be Monday-Tuesday-Wednesday trips all starting about the same time each week, overnighting the same places, returning the same time each week. A reasonable schedule. OR, you could have a 3-on / 3-off schedule, some AM trips, some PM trips, never working the same days, alternating between an early morning schedule and a late night schedule. Not so nice. If scheduling gives you a slate of well-constructed lines to bid on, that's good, but if the lines are all junk, the fact that you get your pick of the junk doesn't make it less so.
ALSO, assigning the monthly awards is FAR from the end of what scheduling does. There is also the "execution" side of scheduling, which means dealing with all the stuff that happens: sick calls, weather delays, maintenance problems, whatever. A good scheduling office can use the tools available to them (reserves, volunteers, reroutes, whatever is in the contract as far as "drafting" non-volunteers on their days off, etc) to cover the flying with minimal hardships for the guys involved (some hardships are necessary, and part of the job). A not-so-good office doesn't handle the unexpected so well, doesn't plan ahead beyond the immediate situation, and treats pilots poorly... "the contract says 8 hours of rest is all I have to give you, so that's all you're going to get" sort of thing. It's one thing to deal with whatever situation you have with the rules in place & moving the markers around to find "a solution"; it sometimes requires a little more finesse and compassion to find a solution that treats pilots as people and not just markers to be jerked around the magnetic board at the scheduler's whim as the plan just keeps on changing and changing. Just because you contractually can do ___ to a pilot, doesn't mean it's smart; the good scheduling departments probably have a better balance of the need to be efficient with pilots vs the need to treat them better than the minimum contractual and FAR requirements. They also can formulate a good plan that minimizes disruptions and won't require six changes before the day is over.
Simple example: if I'm deadheading TO an assignment and the guy flying the aircraft got drafted to fly this one leg & then deadhead home, wouldn't it have been a lot simpler to have me fly this leg, rather than drafting him? Sometimes there are limitations (such as 8 block hours in a duty period) that would prevent such a solution, but if I know there aren't in this case (perhaps I'm not close to any limits that day/week/month), that's a time I might be saying "scheduling could have handled this better."