It's perhaps wrong to generalise on this. It depends on the circumstances.
Airlines Ops have more of an idea (than me, certainly) about reroutes, level cappping and if an a/c is running late or gone tech, but we have a better idea when it comes to taxi times, how much traffic is ahead at the holding point, inbound emergencies that may cause us to go single runway etc etc. We complement each other.
Certainly BA Ops at Heathrow, and thus the crews through ACARS, usually know about updated slot times a few minutes before we get the news from Brussels.
Gonzo.