While people have issues with the +10 damage and I can see it, it at least has a trade-off in terms of the -5 damage. It also has (until you hit 20 Str) the opportunity cost of +1 to hit and damage that an ASI would bring you.
Straight extra damage on every attack on the other hand is just inflating the numbers game. There's no trade-off. It applies to every attack, not just when you have enough buffs going against non-high-AC opponents. Regardless of balance, it doesn't create tension or interest like the current one. It's not an option to chose based on the situation, it's a math fix you calculate in once.
As a though experiment (not a serious suggestion for balance), what if the feat was -10/+20? Would that give enough penalty that it's not reliable even with buffs that it would be a real Faustian bargain? Big risk, a chance to lose all your damage, but a big payoff?
Other thoughts to keep it a choice to be made. -5 to hit & ac / +10 damage. Make it hard to offset all of the penalties without a lot of resources spent. And if you're doing heavy damage, you're a target. (This fits better for GWM then Sharpshooter, since it's easier to focus damage in melee.)
My challenge - fix the feat not only for balance as you see it, but to keep it interesting.