Winning or losing are states, not definitions; what you are in a given moment isn't necessarily who you are, but it can definitely influence your identity. If you let outcomes decide who you are, you're going to have problems--this comes from the very simple fact that you are letting external factors decide your self-worth. It can create a mindset that is very much about avoiding failure, which is not the same thing as a mindset that is focused on achieving success.
I can't say that one or the other is better, but I can say that the former is more fragile than the latter. I've seen it time and again--someone who is winning is a winner, and all the accolades and parades make them feel valuable. But the moment they lose, they become a loser, because nobody is paying as much attention to them.
Is this healthy? Maybe not, or maybe it is just a reality of how all of us are wired a little differently and "healthy" is in the eye of the beholder. Opinions certainly vary.
Regardless of which type of person you are, the one thing you can do to ensure at least some measure of longevity in your journey toward martial arts or competitive mastery is to understand Root Cause Analysis (RCA).
RCA is a means of addressing a problem by finding the catalyst of it through a series of reverse engineered questions. A popular method of this type of thinking is called "The Five Whys" and you see it applied to everything from parenting to exploding space vessels.
In the end, they all examine beginnings to determine how you ended up with the results you did. THIS is the most important thing of all, because it doesn't just make you a better martial arts practitioner--it makes you a better human being.
If you can't do this for yourself or your athletes, you will never achieve long term success, whether you are motivated to avoid failure or motivated to achieve success; your intrinsic or extrinsic motivations will always be at the mercy of time and circumstance.
Every success and failure should undergo a forensic audit that identifies what went wrong, what went right, what are the best practices to be repeated, and what were the systems failures to be corrected.
If you are satisfied with intermittent or transient success, the highs and lows of external approval, then none of this applies. You can ignore the idea of best practices and repeatable behaviors; as long you're winning, none of that will matter.
There isn't much to that lifestyle, but if sustainability isn't an issue, neither is the growth necessary to facilitate it. But if you are focused on becoming better? Then there is no other way to accomplish that other than through analysis.
Root cause exploration accomplishes this for you. It gives you a lens to view your life through that is otherwise difficult to create. And it's worth it, because you will learn so much through that process and create a personal schema that will carry you forward into a future more of your making.
It's through these examinations that you improve upon the things that make you who you are. These roots become apparent and correctable, where need be, or repeatable, if positive, and build you into something greater than what you were when you started. They frame all your learning.
This is how you turn a tournament loss into a learning moment, a win into a repeatable habit, and yourself into a martial artist for life.