That's a tough one. Some coaches will fight to the end; others give up more easily.
If the other coach has more available openings, I rarely do battle. You have to look at his other recruits, however. If he's in multiple battles, you have a better chance. If he has 5 openings, but only 2 players are considering him, you're at a disadvantage
If I decide to go after the recruit, I'll secure my other recruits first, then spend as much as necessary on the contested player