Are both ideal cut? If so, I would go with the 1.71 H. When I got my e-ring, I was looking at a 1.51 E and a 1.65 H, and I choose the 1.51 E. The "mm" size difference was so minor compared to the whiteness of an E, HOWEVER, if it was a choice btwn a 1.51 E & a 1.8 H ( a .29 ct diff like your choices) I would have picked the larger of the two...given both being ideal cut. An ideal cut H, face up is very white.