If there's a tie, then the challenge fails. The point is that if you play an attack card that says "Challenge Power 15" for an ability to take effect, your creature's Power has to be at least 15 points greater than your opponent's Power. So, if your opponent wants to stop you from doing any damage with a card like Ektospasm, they could play something like Song of Treachery or Song of Focus onto the burst you started with Ektospasm, as long as doing so would shrink the gap between your creature's Power and theirs to something less than 15.
In your example, if you're using Frafdo and your opponent is using Rellim, and in the battle your opponent plays Sleep Sting, it would do an extra 10 damage if you do nothing, because the difference between Frafdo's and Rellim's Wisdom stats is exactly 15. However, if you do something like raise your own Wisdom (via Song of Focus, or if you equipped Frafdo with a Ring of Na'arin at the beginning of the game) or lower your opponent's (via Song of Treachery, or in the future, cards with Intimidate: Wisdom), the difference between your and your opponent's Wisdom will be smaller than 15, and the effect of Sleep Sting won't take effect. Does that clear it up?
In girum imus nocte et consumimur igni
