Eliezer_Yudkowsky comments on Harry Potter and the Methods of Rationality discussion thread, part 7 - Less Wrong
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As I understand it, Finite Incantatem is an Area Effect spell, while Finite is targeted.
Additionally, strength definitely factors in--again, as I understand it.
edit: Strength has to factor in somehow. Even ignoring the ridiculous unbalancing effect that would have, they're in Hogwarts. If it would cancel every spell in the area, regardless of strength, Hogwarts itself would be affected with every cast.
Haven't really thought about it until now, but I'll assume that Finite is a brute-force method requiring strength proportional to the original spell to cancel (so a Transfiguration that takes minutes would require a mass casting to cancel, perhaps) and sometimes won't work at all, while specialized counter-jinx just works if the caster has sufficient strength to cast it.
Depends... if the original spell took time/effort due to it being, well, for lack of a better word "delicate", then finite should work easily on it, while a simple spell that you can just pump more and more power into should require a really strong finite to cancel.
At least, that's how I'd imagine it.