As I see it, it is not a competition.
Both Scientology and psychiatry involve very flawed models of the mind and Man, and of the problems of mind and Man, and both involve very seriously flawed "solutions" to these various problems.
Any battle between these two, as some fundamental disagreement of basic "truth", is a contrived appearance.
To me, for the most part, each very much sucks in its own unique way.
I know that in this world where one is often forced to accept either one of only two options, for example, like in the US with the Democrats and Republicans, that it sometimes appears that there are no other choices. But THAT paradigm is a lie. There are many other options, but they are for the most part being blocked from your view (by both external forces and by your own agreement with the limited possibilities offered to you in this current world).