Memory and Indexes

We have two servers replicating the same data from the same master. One is quad (or eight - unsure) cores with 32GB RAM, the other is 16 core with 128GB RAM. Only 8 cores are being used by MySQL.

Interestingly, two totally different indexes were used on each box for the same query. On the 128G box, it was an “in index” index vs a different one. Does memory affect what index is used?

Are all versions, settings, and indexes otherwise identical?