This is the seventh in my comparisons of three headphones, all using a group of 10 tests and scored by ranking their performance on each test as first, second, and third place.  I call this the "Test of the 500s" -- each model number is either equal to or in the 500s, and the cost of each of these is in the neighborhood of $500.
 
Background
 
Here are pointers to the previous tests:
 

• Grado PS500 / Sennheiser CD 300 II / Sennheiser HD-598:  http://www.head-fi.org/t/109756/lightbox/post/10528598/id/1101789
• Sennheiser HD 598 / Beats Studio 2013 / Beats Pro:  http://www.head-fi.org/t/714784/comparing-sennheiser-hd-598-beats-studio-2013-and-beats-pro-quasi-objective-tests#post_10461632
• Sennheiser HD 598 / NAD VISO hp50 / Beats Pro:  http://www.head-fi.org/t/714904/comparing-sennheiser-hd-598-nad-viso-hp50-and-beats-pro-quasi-objective-tests#post_10465009
• Parrot Zik / Beats Studio 2013 Wireless / Sennheiser PXC 310 BT wireless / noise canceling:  http://www.head-fi.org/t/715959/comparing-wireless-noise-canceling-headphones-parrot-zik-beats-studio-2013-wireless-sennheiser-pxc-310-bt-quasi-objective-tests#post_10487062
• Grado PS500 / Stax SR5 with SR6 Driver / Klipsch S4i IEM: http://www.head-fi.org/products/stax-sr-5-with-srd-6-adapter/reviews/10909
• Klipsch S4i / Apple In-Ear / Apple Earpod IEMs:  http://www.head-fi.org/t/716814/comparing-iems-klipsch-s4i-apple-in-ear-hps-and-apple-ear-pods-quasi-objective-tests#post_10505338

 
Here are the overall results, expressed as rank orders, of the above tests, with top scorer of the three comparisons in blue, second place in red, and third place in yellow:
 

 
 
Comparing Sound Quality:
 
Because the HiFIMAN HE-500 demanded an amplifier, in the following three-way test I used an amplifier (FiiO E12 "Mont Blanc") with all three headphones.
 
I used four songs:
 

• "You're Going To Miss Me When I'm Gone," by Band of Heathens, from their album One Foot In The Ether (used for fidelity of drum sound, positional resolution of two vocalists, and ability to discern pitch of string bass passages);
• "Spanish Harlem," by Rebecca Pidgeon, on The Ultimate Demonstration Disc of Chesky records (used to assess female vocals, transparency, the attack of finger on bass string, and high resolution discrimination of differences in shaker shakes);
• "Symphony No. 3 in C Minor Op. 78 (Organ Symphony) - IV" by Camille Saint Saens played by Lorin Maazel and Pittsburgh Symphony Orchestra (used to assess the "ripping" sound of well-rendered lower brass and organ reed pipes, and the ability to hear a very small entrance amidst a bombastic chord of orchestra and organ at full tilt);
• "Throwback" by B.o.B. on Underground Luxury (used to assess ability of a bass tone, specifically lowest C on piano at about 32 Hz, to pick me up by the throat and shake me!)

 
The 10 tests were as follows:
 

• Transparency:  What is between me and the music?  A felt cloth?  A "Sennheiser veil?" A frosted window?  Dirty window?  Clear Saran wrap?  or nothing?  At its best, makes me forget I am listening on headphones and am in room with musicians.
• Width of sound stage:  How far to the left and to the right, (yes, AND up and down in best cases) does it seem the musical sources are arranged?
• Positional resolution:  Can I distinguish a difference in position of two singers in Song 1?
• Bass visceral:  Does the bass in third verse of Song 4 actually shake me? Or do I just hear it?
• Drum "twang":  At start of Song 1, do the bass and tom tom drumhead have a tone and a pitch, rather than just a thump?
• Bass pitch perception:  For the complicated bass runs in Song 1, do I hear a pitch with sufficient accuracy to sing or transcribe the part?
• Bass finger pluck:  Do I hear the actual impact of fingers on the bass string just before hearing its sound on Song 2?
• Shaker variation:  In Song 2, verse 3, do the various shaker shakes sound a bit different from each other, as they should?
• "Ripping" of organ / brass:  In Song 3, is there the sensation of hearing each vibration of the French horn and low organ reed tones (sort of the tonal counterpart to hearing a "pitch" from a drumhead in Test 5);
• Discern added chord:  About 1:38 into Song 3, after the full orchestra and organ hold a chord at the top of a passage, can I hear a small number of orchestra instruments join in, as sort of an echo, in the second measure of that chord?

 
These tests generally emphasize what I find most pleasing in a headphone, namely high-frequency-related features including transparency, upper harmonics of sounds from drum-head, brass, organ pipe, and string bass, and high-resolution effects such as fine detail of each shaker sound and the finger on the bass string.  Only one test (#4) appeals to my emerging "bass-head" nature -- hence bass response is under-represented in these tests.
 
Headphones Tested:
 
Because the HiFiMAN HE-500 requires an amplifier, all three headphones were tested with an amplifier... the FiiO E12 (Mont Blanc), set with 16 dB gain and zero bass enhancement.
 
HiFiMAN HE-500:  In short, these are the first of all headphones of the 16 or so tested to simultaneously provide the high-frequency characteristics of most of the tests and bass that is strong enough to start to be felt as well as heard.  They are a bit heavy over long times.  Their planar magnetic drivers (as opposed to dynamic drivers of the other two) are lower efficiency and benefit from an amplifier, though they do give good sound at medium volume from an iPod Touch 5th gen without an amp.
 

HiFiMAN HE-500 (list $699 / amazon.com $599).
 
Grado PS500:  These on-ear headphones excel at transparency and high-frequency resolution.  They are light on bass, but their high frequency response still allows accurate detection of higher bass harmonics and hence bass pitch and timbre.  Their heavy cord outweighs by a factor of two the iPod Touch 5th gen that these headphones are easily driven with (no amp needed).  On-ear becomes tiresome over time.
 

Grado PS500 (list $699 / amazon.com $650)
 
Shure SE535 Bronze: These in-ear monitors have three dynamic drivers inside, each tuned to a different portion of the frequency spectrum.  They require a bit of skill to insert, but block out exterior sound and are reasonably comfortable.  They also come with a thinner cord that includes iPod remote functions in line (volume, advance/repeat, pause), not shown here.

Shure SE535 Bronze (list $539, amazon.com $468)
 
Test Results:
 
The table below scores the performance of each of the three headphones on each of the 10 tests.  The best-performing headphone received a score of 3 on a test; the worst performing was given a 1.  Ties were given equal points.
 

 
The Shure IEMs scored the  highest, showing excellent performance in the high-frequency attributes mentioned earlier.  Their ability to handle deep bass was quite limited - their score of 1 vs. the 2 and the 3 of the other two headphones was quite a distant third.  However, they sparkled in the myriad of other tests.
 
The Grado PS500 provided delightful response to the high-frequency features with a bit more bass presence.  The HiFiMAN HE-500, as stated above, is the only headphone so far to offer both excellent response to the high frequency features and enough bass response to start to be felt viscerally as well as to be heard.
 
So the results of the test can be summarized as an additional row in the introductory table (first, second, and third highest score) as shown below.