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Both lines are +EV, given the current size of the pot. The fact that deciding between the two is "close" or "hard" is not a good reason to muck this pre-flop.

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This statement is absolutely correct. I have explained my general philosophy of why I prefer checkraising over betting, but both these plays are close and both are +EV.

What about folding preflop with our 97s. Is this a viable option? Given the action preflop, the hero's hand is simply too strong to fold getting 5-1. Since the button is isolating a single limper, it is very unlikely that an overpair is out, which is why the hero must call and participate.
Now if you change the action preflop I would fold 97s in the BB getting 5-1. For example if a TAG raised UTG and another TAG coldcalled UTG+1 then I would fold, becuz the chance an overpair is out is just too high for me to continue even getting 5-1.