How to make Minimizer search more precisely

Dear experts

I have two minimizer that using 4 parameters where 1 of them is different between minimizers. When I try to minimize the chi2 by 2 minimizers I got different but close results, I doubt that maybe there are some local minimum caused the difference, is there a way to make the Minimizer do the minimization with more carefulness?
I already set the SetStrategy(2) in the minimization.

Hi,
@jonas should be able to help you with your question.