I'm gonna assume Colorado. You will find 2 different beliefs, and both are right, just depends on how confident you are with your technique.
Some say earlier because the herd bulls don't have all of their cows yet and they are easier to get within range of. Also they say that they are more likely to come to your calls since they don't have to worry about their cows yet. If you are hunting the earlier time, I'd definately try and find the wallows and think strongly on using Whitetail tactics, as in sitting on your butt from 1 hour prior to sunrise to 1/2 hour after sunset.
I like to hunt after. Seems to me that they are more responsive to calling. The reason is directly related to the weather, which is more likely to be cooler. The peak of the rut is always at the same time of year(calves are always born around the same week right??). When the weather cools however it just makes them more active and responsive to calling. Also I hunt where the pressure is minimal which really helps.
With that being said, the most important factor is hunting ALL day, don't hunt for 1 hour in the morning then walk back to camp and hunt 1 hour in the evening, Stay out there the ENTIRE day.
Use your time wisely and scout while you are out there stalking. Watch to see what areas they are currently using and why. That way as the season wears on you can constantly fine tune your strategies.
Mntman
"Hunting is where you prove yourself"