My guess is that the competitive private club could be better recruiting-wise than a HS team.
It may be worthwhile to chat with a coach on the private team – it is early but it never hurts to get an idea of how the recruiting process works, how the team supports its members, etc.
FWIW there are many examples of sports/areas where club teams are more competitive/elite compared to the HS team. This is not an unusual situation.