Whether constant tension or full ROM chins are better would depend on your goals (why you are doing the exercise). Generally though I think that most people should do full ROM (deadhang) most of the time as they will help keep the shoulders healthier and maintain shoulder mobility more effectively.
You are incorrect though that partial ROM chins require more work than full ROM chins as "work" has a distance component and the distance travelled during full ROM chins is greater (the weight obviously remains the same in both versions). So full ROM chins actually require more work from the lats.
Both movements work both muscles but to different degrees.
I would say the ROM could be longer. I don't like dead hang pull ups but going down to the point where you have a slight bend in the elbows is fine. from there, pull yourself up smoothly until you get to the highest position you can get. contract at the top for a moment and really squeeze, then go down again. I can do about twenty chins the way you do them in this vid; the way I do them I'm usually done after twelve.
My take on it: While it is true that work is the dot product of force and distance, in this instance however I am not sure whether the few extra inches of distance would translate to work done by the lat muscles - what I mean by that is at the very bottom range one usually relaxes the shoulders and shifts the tension from the lats to other small muscles and ligaments in the shoulder area.
Plus constant tension allows you to do a few more reps overall (increasing TUT and useful work done) making the strength of the lats the limiting factor in performance, whereas in the deadhang version you cut your set a few reps short usually because of fatigue in the forearm muscles and end up doing less actual useful work for the lats.
Which is why I said I'd go down until there's a light bend in the elbows. The lats are still under tension at this point. You're actually making the movement easier for the lats because all they really have to do is contract by 1-2 inches.
The involvement of those smaller shoulder muscles is why deadhang chins are better for overall shoulder health.
Also, the lats actually are always under constant tension when performing chins (partial ROM or deadhang) as they originate on the spine and scapulae and attach to the Humerus and at no point do they detach from either of those two points). What changes is the degree of leverage that they possess and the number of Actin/Myosin cross bridges that are in contact at different points along the ROM. What you are essentially doing is staying within the "strong" portion of the ROM (where your lats have good leverage and a good number of cross bridges in contact) to allow yourself to get more reps (and yes, keep the muscles under tension longer). This would be akin to performing quarter squats or top 1/2 bench presses to get more reps and keep the muscles under tension longer.
Which is fine to do if that fits your goals.
Again, you are getting more reps because you are never forcing the lats to work outside of their "strong" ROM, not because they are under constant tension (which actually should result in fewer reps in theory as implying non constant tension would be definition mean that the muscles are getting to rest between reps).
If you are really worried about the forearms/grip limiting the amount of effective lat work during deadhangs, then just use straps (that's what they are designed for). Or, realize that your shoulder mobility or grip strength is poor, and that you need to work on it (if strength or performance was your goal).
Both movements involve elbow flexion and shoulder extension/Adduction (depending on the width or the grip and degree of supination/pronation of the forearms), so both involve the lats, Teres Major, posterior deltoid, and arm flexors.
The difference is that with the forearms supinated (chins) the biceps are placed in a position of mechanical advantage and will therefore be better stimulated, while when the arms are pronated (pull-ups) the biceps are in a position of mechanical disadvantage and therefore the other arm flexors (brachioradialis primarily) instead become the primary arm flexors (think regular curls vs reverse curls). Both variations involve the lats equally though.
Sentoguy: While it is clear to me that deadhang chins (or full rom in every other exercise for that matter) should be the norm, I would like to ask you this.
Working in a ROM where you have greater mechanical advantage for the main muscle group trained ( that is a greater number of actin-myosin cross bridges formed within the sarcomeres along that specific ROM), wouldn't this greater amount of cross-bridges along that rom translate to a greater potential to induce micro-damage (since a greater amount of myosin proteins are "pulling" along the actin filaments) when compared to doing the same amount of reps with a deadhang/full rom?
Or is it that the fewer cross-bridges in the rom where you are at a disadvantage (leverage-wise) mean that the smaller number of cross bridges formed must share the brunt of work and pull stronger (individually) and hence eventually have greater potential for inducing microtears/hypertrophy?
I'd say just personally, if doing chins to hit mostly lats, I'd cut the top 1/3 of the ROM out, not the bottom. I feel the top part, once getting your forehead/chin past the bar is when biceps take over. But I also have long arms, to could be different for me.
That's an interesting question. Your logic seems solid, but anecdotally exercises which emphasize stretching the muscles (incline curls, pull-over extensions, "droop rows", etc...) tend to produce the most DOMS (when first introduced, of course the body eventually adapts to them and there is less soreness). Eccentric speed also tends to be a big factor.
The exact reasoning for this is unknown (to the best of my knowledge), but I'd assume that it has to do with the greater total number of cross bridges that get "pulled apart" from gravity due to the greater range of motion. Again, just my best guess though.