You are correct. The direct mechanical advantage of a 44-16 is the same as a 33-12 or even a 22-8, because they all share the same ratio of 2.75:1. Given that, there is a slight mechanical adantage at the point of chainring to chain with a larger chainring. The crankarm and the chainring work together as a Class 2 lever. Consider a prybar jammed under a big rock (also a T2 lever): the deeper you push the prybar under the rock, the better advantage the lever has versus the load (the rock). A longer prybar (crankarm in our case) will prove a much better overall mechanical advantage.
Summary: assuming the same gearing, is there a measurable difference in chainring sizes? Yes. Is there a noticeable difference? Probably not.
-Paul