I hear a lot of frustration caused by two people doing the same task differently. Something like: I start with the big picture, he starts with the details. I start later, she starts sooner. And so on...
It is often coming from a vantage point of "I do it right, they do it wrong" because we all do the best we can, and think we do things correctly.
Questions to ask:
Is the other approach actually causing any harm?
Does it to get a "good enough" result?
If it is not harmful and the result is good enough, acknowledge that there is a different way and move on.
The other way might actually be decreasing a blind spot.