rear wheel has a lot more going on (freehub pawls etc) but it should be close enough to the same smoothness that you can't feel a difference in your hand.
You might need to go beyond just tweaking the cone tightness, and actually open it up and get some lube in there.
What kind of bike is this? If it is a bike-shaped-object from walmart, it is absolutely expected for hubs to be misadjusted, and even when adjusted as well as possible, not very good. If it is a 'real' bike, new hubs still might be overtightened, but with proper tension they should be fine.
My rule of thumb for amount of play to shoot for is a few mm wobble at the rim. Tighten that up with quick-release, and it should go away.