So I've had the MKIII for a couple days now and have some first impressions vs the Darkvoice 336i.
First of all, a few disclaimers: the Darkvoice is optimized to my liking with Svetlana 6H13C and GE 6SN7GTB tubes, while the MKIII is stock. The total cost of ownership of the Darkvoice with my tube collection is roughly twice that of the MKIII.
Source was a Benchmark DAC1 USB with foobar playing LAME VBR MP3's from the PC. Most of my listening was done with an AKG K701, with some DT990 05 (250 ohm), and MS2i thrown in. Music: Jazz, vocal jazz, rock, classical, ambient, hip-hop.
Build and cosmetics: The MKIII is every bit as nice looking in real life as it is in pictures. Build quality and design are very good IMO. Little Dot has come a long way here from the LDII series. The MKIII looks very nice next to, or on top of, the DAC1. The MKIII is considerably lighter and a fair amount smaller than the Darkvoice.
Soundwise, the MKIII is more forward, solid-state-like, fast and punchy sounding. Transparent but with nice tubey liquidity, if not tube warmth. Closer to the headphone out of the DAC1. Not bright but can be harsh with a few poorly mastered recordings. Contrary to one review, I really liked this amp with hip-hop, bass is fast, tight, and punchy here. Not entirely black, with the volume down you can still faintly hear music from the DAC. The pre-out is surprisingly competent, much better than the DV336i.
The DV336i is darker in comparison, with more nuanced and prominent low frequencies, more powerful sounding. With my tube upgrades, slightly more resolving across the spectrum. Overall this sound is more to my liking. I am slightly biased to a warm and weighty sound. Tube upgrades are key for the DV336i, though, with stock tubes it sounds a bit veiled and muddy IMO. Soundstage accuracy seems about equal with both amps. The pre-out on the DV336i is quite poor to my ears, with a slight hum consistently.
My early verdict on the MKIII: This amp is a phenomenal value for money. It's hard to imagine a better performing amp in this price range. Build quality and sound quality are delightful for the price. The K701's are not the best match for this amp, being very slightly leaning towards a treble emphasis. The MKIII pairs better with the DT990, with more bass presence. The MKIII would likely pair very well with Sennheisers. Unfortunately, I don't have access now to my HD650's, so I haven't been able to try these. With the MS2i I slightly prefer the DV336i.
So how about tube upgrades for the MKIII? My hunch is that this wouldn't change the MKIII as much as tube upgrades have for the DV336i. The 336i is reputedly sensitive to tube changes, and in stock form begs for tubes upgrades, being a bit veiled stock. The MKIII is already very transparent sounding out of the box. I suspect the stock tubes are well picked and already relatively good, adding to the great value of the MKIII.
Sorry for being the evil one! 
