as someone who plays SMN on main you'll definitely do better on a movement heavy fight with SMN than BLM.
Not strictly true tbh. A SMN might have an easier/quicker time learning and optimizing a fight than a similarly skilled BLM, but when played at the highest level BLM will contribute superior damage, even in fights that are movement heavy. There's always a way to maintain DPS even in the midst of mechanics.

Sephirot is a great example of a supposedly movement heavy and difficult fight for BLM. See the following link: http://www.fflogs.com/statistics/4#boss=1031&dataset=90

SMN is ahead until you reach the 90th percentile of players. BLM catches up here; and slowly but surely pulls away from SMN in the 95th, 99th, and max percentiles, approaching even monk levels of DPS. The only fights I see SMNs consistently beating BLMs are fights full of aoe opportunities (A2S), because BLM single target DPS is monstrous even when slightly gimped by movement or mechanics.