"Beat Competitor X" is always the wrong kind of goal to set.
It's a bad goal because it's not something that's in your power to deliver: you can beat the competition simply by standing still if while they hit a major problem, or similarly, you can vastly improve your performance, yet "fail" to beat the competition simply due to customer inertia or anti-competitive behaviour by competitors.
Bad high-level goals promote bad low-level goals. "Beat Competitor X" becomes "Ship more of our product than theirs". That's a bad goal because there are easy, and destructive ways to achieve it. Like discounting the product right down to its cost of production: Well done, you've met the goal, and left your company without cash for future investment. (Hello, General Motors!)
Toyota follows a very simple, iterative system: every year, you have to be better than last year on a series of measures. A clear goal, and achieving it depends only on your own staff - no outside factors. This is the same approach that FCA has adopted (although within the framework of WCM it's framed in terms of reducing "waste": activities and materials that do not improve the company's products). It's a long slog, and you need to get everyone on board (difficult in a Western manufacturing culture of "us" on the floor and "them" in the offices) but it pays off in the end.
The one time Toyota departed from this approach was in the early 2000s, when the corporation set an arbitrary goal of 5% more sales, 5% increase in gross profit per sale, all within five years. This was the time we had the rusting truck subframes, unintended acceleration and other un-Toyota quality issues. Toyota had abandoned suppliers with whom it had built decades-long relationships, and went with new, cheaper companies; the problem was that the older suppliers worked collaboratively with Toyota, often bringing potential design issues to Toyota's attention, and working to redesign parts around those problems before beginning production. The newer suppliers just made what they were told to make.