Good headphones in the around - $100 price range should provide better sound athan $40 and  below priced headphones. They should also have a remote and mic and be of a quality build.

The best in-ear headphone under $100  for iPhones: Marshall Mode In-Ear iOS (mobile-OS specific single button remote to answer calls, handle music playback functions, and activate voice commands., balanced sound profile)
The second best in-ear headphone under $100: 1MORE Triple Driver In-Ear Headphones (three-button remote, more intense highs in bass treble)
The best in-ear upgrade: Sony XBA-H1 (without mic or remote)
The best affordable in-ear headphone: AKG Y20U from Harman Audio