Without knowing more about your system... both seem to give similar answers.
hi2 = [15.8407983652723 224712.855054258 49190.7060861108 -139558.381444911 -182685.449767951 -14593.7826296176]'; >> (h2-G2*phi2)'*W2*(h2-G2*phi2)
ans =
0.61067314010686
>> phi2 = [0 224658.368498995 49166.3250817687 -139602.451899739 -182822.341031919 -14652.8624815402]'; >> (h2-G2*phi2)'*W2*(h2-G2*phi2)
ans =
0.610669863650048
Both algorithms give you very similar objective functions with different values for phi, which suggests both are doing similar things. Why, they get to the same answer with different values of phi2 is much more complex.
We know that a simple, 2nd order polynomial has 2 roots. So is it surprising that your set of equations/constraints has more than one mathematical answer?
Not knowing more about your actual equations, it appears that your first variable may be less significant than your others with respect to minimizing your objective function.
If this is a physical system, one would hope to have some reality checks in the values of phi2. Like if phi2(1) was a mole fraction, then the being outside 0 and 1 would simply not be physically true. Again, without knowing what the system is physically it is hard to comment.
Is there any reason to believe that phi2(1) is relevant to describing your system?
