One set, EarHeros, claims to be the "world's most elite earpiece" and has a price tag to match: $150! But when testers assessed this "elite" set, they has the worst sound of any headphones Consumer Reports tested. The bass is lacking, and it's a little bit harsh sounding. In fact, despite being the highest-priced non-isolating headphones tested, the EarHeros are the lowest-rated, with an overall score of just six out of 100.
There are many non-isolating headphones that provide full-range audio, which lets you hear bass, midrange, and treble pretty much the way they are supposed to be heard. Apple's basic EarPods rated much higher, and at $30 cost far less. For even better sound, Consumer Reports recommends the Bose IE2 headphones. You'll get very good audio, and at $100, they are still less expensive than the EarHeros.
If you're looking for headphones to use inside and want noise-canceling ones that block out other sounds, you'll have to spend more. Consumer Reports recommends Beats Executive from Beats by Dr. Dre. They have an over-the-ear design and deliver excellent sound quality and very good noise reduction for $300.