The Nissin Di622 mk2 is the sequel to the fine-enough Di622. Owning a Di866 myself, and having good experiences with it, it was quite a simple decision to go for Nissin again.
The Tumax DSS688 was the unknown, though judging from the construction it should be quite similar in innards to other brands like Dörr. What must first be clarified is that the Tumax is an all-manual flash. No e/i/anyTTL or automation of any kind.
Let's start with the similarities. They have similar guide numbers, the Nissin with 44 (m) at full 105mm zoom, and the Tumax with 45 (m) at 85mm zoom, according to their respective spec sheets. It is however difficult to do a real comparison between them, since there is no manual zoom on the Nissin. According to the manual, when you direct the flash head in any other orientation than front, the flash head sets itself to 50mm, which I assume it also uses when used off-camera.
The flash head is also where the DSS688 departs from all my other flashes, in that it does not have a motorized zoom. You take the flash head and pull it out to zoom the flash.
They also have very similar connectors, both coming with PC socket and 3.5mm sync port. While this may seem all well, readers of the Tumax manual will soon find a large minus. The ports are namely separated, so the PC socket is output only, and the 3.5mm is input only. With the Nissin you can chain it however you like. The Tumax however is packaged with two PC-to-3.5mm cords, which gives it some plus-points back.
The build quality for both is pretty standard plasticky. Neither matching up to the Di866 (which in turn doesn't match the sturdiness of my SB24's). The Nissin feels a bit more solid though. The buttons on the Tumax are also not very confidence-inducing, and the small light that you can activate to light up the display falls short of lighting it up...
Using them off-camera, you have plenty of options for both, but in very different shapes. For its basic approach, the Nissin holds some nice options, changing the mode at the push of a LED-lit button, which changes colour depending on which mode is selected. A simple, but effective approach that makes good use of the little space is available at the interface panel. There's manual, for radio/wire triggering, slave digital for TTL-triggered, the "dumb slave" mode for trigger on light, and a basic wireless mode that puts it in a fixed location of channel 1 group A.
The Tumax takes a completely different approach. Instead of any automation, it simply has 9 different slave modes, with each mode ignoring that number of pre-flashes (with 0 being the "dumb slave" mode). While this mode can be trickier to deal with than the TTL-based slave mode, it does give the user the option to use this flash together with other TTL flashes regardless of brand.
In many aspects, the Tumax is the odd duck next to the beautiful swan of Nissin, but the Tumax has an ace up its sleeve. Hook it up to a DC power converter and you can shoot it without batteries for as long as you want (or until the flash melts). This I would say is the main selling point for the Tumax: hook it up to the wall and worry no more about whether you brought enough batteries or not. Assuming you're staying indoors, of course...
In summary, I would not recommend the Tumax unless you know what you're doing, but it packs a real flash beneath its rough outside and basic controls. The Nissin on the other hand is a fine flash for both beginners just starting out and pros wanting to add another light, it's cheap enough and the features are just right to allow for some serious connectivity. Zoomable flash head in manual mode would have been nice, but for the price, it's plenty flash. Besides, there's always go-bos...
UPDATE: After having used both, the Nissin far more than the Tumax, I have more and more come to think that the Tumax really falls on its own sword. It is, in fact, my least used flash. While the wall-wart option is interesting, it still suffers from the longer recharge times like other models, even when using it. Then you have to ask yourself whether it's a better option to just buy a studio strobe head straight away. (Looking around here I see an Elinchrom D-lite 2 head for less than double the price of the Tumax.)