A "Smite battle" is when both junglers are at the objective, both have Smite up, and whoever clicks Smite at the right moment wins. This is a 50/50 coin flip. Good junglers never take 50/50s.
How to avoid Smite battles:
• Kill the enemy jungler before starting the objective. Sounds obvious, but most junglers don't do this.
• Zone the enemy jungler away. Have your support or tank stand between the objective and the enemy jungle entrance.
• Burst the objective from 2,000 HP to 0. Coordinate with your team: "Burst at 2k." The enemy jungler can't react fast enough.
Smite does about 1,500 true damage to monsters at level 15. Know your Smite damage. When the objective hits 1,500 + (enemy burst damage), Smite it. Don't wait for it to get lower — the enemy will Smite first.