No. In The Santa Clause, friends and family of Scott do believe he's crazy for thinking he's Santa (or looking like Santa), but in fact, Scott was established as Santa early in the movie. We as the audience knew he was the new Santa.
In Miracle, it was never established until the end that Kris was real, and even then, it was only a suggestion based on circumstance.
Did the success of the Santa Clause cause audiences not to like this movie as much since it is similar film and was released at the same time?
I don't see any relationship at all, unless one wants to suggest that there are only so many Christmas movies moviegoers are willing to see in any given season.
To me, this movie didn't do well because it's simply not a very good film, and nowhere near as good as the 1947 version. A remake should either be better than the original, or at least having a unique take on the same story that would make it interesting. This film does neither.