My friend and I were playing clix a few weeks ago and this issue came up:

My Rogue/Gambit duo used their Charming Rogues power to outwit the standard outwit of one of his figures. Could I then use the outwit to outwit yet another power? He argued no, as I was using the same game effect twice. I argued yes, as they are technically different powers and rationalizing that since the effects of a special outwit (like the new Leader's double outwit) is negated after losing it, only to gain standard outwit, then I gained a totally separate power with similar effects. As always, the power is described below:

CHARMING ROGUES: Gambit / Rogue can use Outwit targeting only adjacent characters. If they do and they counter a standard power, Gambit / Rogue can use that countered power until your next turn.

From the Rulebook under Free Actions.

Is the effect of each outwit the same?

The question is not "is the effect of each outwit the same?", the question is "are you activating a game effect (Outwit) twice in one turn with a free action?" And you would be, so you could not do that.