I'd probably take average strategy with strong emotional control.
Elite strategy doesn't help much if your emotional state prevents you from consistently executing it. And poor emotional control doesn't necessarily mean obvious tilt or huge punts. It can be subtle — playing too many hands after a loss, rushing decisions, becoming overly cautious, chasing losses, or simply losing focus.
That said, I don't think it's really either/or. Technical skill and emotional control amplify each other. The stronger your game becomes, the more important it is to be able to access that skill consistently under pressure.
For me, the interesting question isn't whether you ever get emotional — that's inevitable. It's how quickly you recognize that your state has changed and how reliably you can get yourself back to your A-game.