Great question. Early on at The Rum Project, we became fascinated with this question - we literally spent months trying different glasses and learning all about glasses from a wide variety of real tasting experts. All of this experience was then later summarized in my E-Book on rum, in "Chapter Three: Tasting and Glasses" (link
In this very long chapter we cover the many, many different types of tasting glasses, and which ones the real experts prefer and why, plus our own conclusions and personal favorites. There are good reasons why certain glasses work and others don't. One closing thought: if you don't think glasses make much of a difference, try the same rum from your two glasses, plus say an ordinary small wine glass and also from a tumbler.
You'll hardly believe its the same rum. BTW, the Count's choices are good, particularly the copita. Good luck!