I will personally recommend to use the result (lattice parameter) after the fit with the Birch-Murnaghan equation, that what people do especially the bulk modulus will be included as a result and compared to experimental data. Your obtained energies are sampled with discrete lattice parameters, except the case when your step is very small, your derived lattice parameter will always be approximate. The BM equation is continuous and has an identifiable minimum.
However, I noticed that the results are slightly different by 0.0926 Angstrom.
The error is relatively small, you may find it large compared to experimental results for example, but it is really small compared to the non-negligible error induced by an approximate exchange correlation functional.
I wonder why they are not exactly the same?
A macroscopic classical and a microscopic quantum result will never be in perfect agreement.