Efficiency is rated at 93db vs 98db for the HE400S, most of the reviews that I've read and watched recommended using the 400i with a headphone amp. My Dragonfly would drive the heck out of a 400S.
For now I'm in no rush to pull the trigger on anything. I have really-really good IEMs and closed back headphones that I mainly use at the dog park and while enjoying a latte at the coffee house. I'd like to pick up a newer set of open-backs but I'm not in a huge rush to do anything. I don't need them, but I'd kind of like a set for when I'm relaxing in my yard in a lawn chair. Again, no rush.
I ran my HD500s off a receiver (my old portable headphone amp struggled) and they sounded pretty good with the receiver but I always felt that the HD500 would sound even better if driven off a dedicated headphone DAC and amp. I'm probably not going to buy anymore headphones or a headphone amp this year, but just in case another deal of HD600s pops up, I've been thinking about a Schiit Audio's Modi 2 DAC and Magni 2-Uber headphone amp. Not exactly super high-end but I would think this would be plenty of power for the HD600 at a reasonable price, I could be wrong though.
http://www.schiit.com/products/magni-2
As an FYI these are the specs for the Magni 2 Uber:
Frequency Response: 20Hz-20Khz, -0.1db, 2Hz-250KHz, -3dB
Maximum Power, 16 ohms: 2.1W RMS per channel
Maximum Power, 32 ohms: 1.5W RMS per channel
Maximum Power, 50 ohms: 1.2W RMS per channel
Maximum Power, 300 ohms: 320mW RMS per channel
Maximum Power, 600 ohms: 160mW RMS per channel
THD: Less than 0.002%, 20Hz-20KHz, at 1V RMS
IMD: Less than 0.003%, CCIF
SNR: Greater than 104db, unweighted, referenced to 1V RMS
Crosstalk: -70dB, 20 Hz-20KHz
Output Impedance: Less than 0.2 ohms
Gain: 1.5 (3db) or 6 (15.6db), selectable via rear switch
Preamp Output: Yes, controlled by volume pot and switched via headphone jack
Topology: Fully discrete FET/bipolar, constant feedback through audio band, complementary VAS drive, Class AB, DC coupled throughout
Protection: Standard failsafe DC power input and muting relay
Power Supply: “Wall wart” style 24VA 14VAC transformer, regulated +/-15V rails, with over 6,000uf filter capacitance
Power Consumption: 5W
Size: 5 x 3.5 x 1.25”
Weight: 1 lb