Why are they exactly the same?
Have u deduce the final solution yet ?
Let's check a single pole system,
A(s) = A/(1+s/p) --- Open Loop
I think the close loop should be like this,
(A/1+A)*(1/1+s/A*p) --- Close loop
As u can see,the former part in equation is affected by DC gain.
Maybe there is some misunderstanding between us.And I think in your transient simulation,
the DC gain of your OPA was set too high to miss the difference of two OPA system.
e.g 1000/1001 and 2000/2001, some time it's hard to track this.