I just got a pair two days ago, I am not an experienced audiophile (recently got the virus) but I have always been a lover of good sound and I have owned mid-fi gear up to a few weeks ago.
After two days of intensive use, my first impressions are good, but those are the first open back headphones I have ever owned which means I don't have a basis for comparison (except for the Philips Fidelio X1 I got for a week before I returned them for the Shures). Just for the record I went for the X1 because it had low impedance (and my headphone amp equipment is not there yet) and high sensitivity, also reviews were rather good and I like a warm and sweet sound (got a pair of closed back Momentum, love them). In the end for me the X1 had too much of a V shaped signature for me, too dark sounding.
I hesitated a long time between HD650 and the SRH1840, and went for the later. The fit is just amazing it feels like you're not even wearing them unlike the X1, kudos to Shure. Soundwise, so far I am not disappointed, one question mark was the bass, the Shures were said to be below what the HD650 delivers, but I was weary about buying hard to drive headphones that would require me to spend even more cash on my newfound passion
It's still early but I noticed no sibilance and I am sensitive to harsh trebles and I have not found any occurence of that with the SRH1840. As for the bass, I am quite satisfied there is enough of those for my taste (less than the Momentum but can't compare to a closed back, obviously the bass are way more subtle in terms of instrument separation, decay...). Anyway, it's not bass weak to my ears, it's up to toe tapping level
The sound is more balanced than the Phonak PFE 232 I own, the mediums are really nice, I welcome the different listening experience in that regard.
I am driving the SRH 1840 with the Sony NSW-F806, and I was suprised that my wolfson powered Galaxy S3 is able to drive them (though pushing it near the volume limit).
I have not yet invested in a "proper" headphone amp (but I have purchased Audioquest Dragonfly to listen to music on my Mac). I must say although I love the Dragonfly, it makes the Shures sound too analytical to my ears (the Sabre ESS chip maybe...).
I have also tried the FiiO E6 with Galaxy S3 and I kind of like the warm sound that comes out of it (but nowhere near as detailed and punchy in the bass department as the Sony player).
My next purchase might be the Carot One Fabriziolo amp (http://www.head-fi.org/t/614862/carot-one-fabriziolo-small-tube-amp), a tube amp seems like a good idea to get a warmer sound from the Shures. Wonder if anyone has tried that combo or has a amp suggestion for the SRH1840 ?