Many people have complained about legibility issues with Helvetica Neue in iOS 7 & 8. (Though I have no issues and in fact did not like the later increase in font weight).
SF is rather similar to Helvetica Neue, but it is further tweaked to enhance legibility at small sizes. Hence SF Compact (on WATCH), and text at small sizes with increased weight in iPhone look especially different from previous versions.
You can especially appreciate the beauty of SF when it is used as a display font at large sizes. Too bad there were so many complaints about Helvetica Neue, plus the usage of Helvetica Neue could be so easily copied by other companies.