In most systems of die classification, the two coins pictured represent the SAME die style. The same eagle and the same cap are used. The letter fonts are different and the Star at the denomination is a different shape. But those are normally considered to be minor die variations (sub-types) - interesting but of no great difference in value.
Each die in 1877 at Alamos was somewhat different and that means that no two die pairs match exactly. But how many dies were used that year 50 - 100 ?
In the case at hand, the leaves and vines also show minor variations - but the Cactus seems to be identical.
What you see with these two coins are dies that were finished by different workers using different letter sets. The A at the end of MEXICANA is particularly interesting. On the coin shown first, it appears to be partially hand cut. It does not match the other A's.