Rivalry? Not even close
How about we compare recent history, say starting in the 80s?
Series history: Bama leads 18-15-1
# of SEC FB titles: Bama (4 outright & 2 shared)
LSU (5 outright & 1 shared)
# of AP/coaches' nat'l titles: Bama (3/3)
Counting games & seasons from more than a generation ago says little about the state of a series as it stands now. Among other SEC members, only Florida has had the same high level of success vs Bama & in general. By your line of reasoning, Bama-Auburn & Bama-UT aren't rivalries either since those 2 have experienced less success than LSU has in comparison to Bama.