skill differential? what do you even mean? How do you measure it.....or attempt to? Tkachuck is absolutely not lacking in the skill department. The early knock on his was skating and he's improved considerably since breaking into the league. Pettersson is trending in the other direction.
over the last 3 season, Tkachuk has taken 2x as many high danger shots and has, as a result scored more goals (85 vs 80). Maybe you can explain why goals and high danger shot generation should be considered secondary traits? It's not like the team with the most "slick dekes" wins the game.
As far as who's the better defensive player, it's hardly clear cut IMO. Brady's +/- is not great, but his - team leading - shot attempt differential is miles better (+654 vs +152).
It isn't like he's some knuckle dragging unskilled crash and bang winger we're talking about, he has high end offensive skills in addition to the physical game. kind of like if JT Miller was the same size as Tom Wilson.