I'd say simple tactics all the way, at least until you can do every tactics trainer in 5 seconds (but I don't believe any of us can!). See, just getting into your head thousands and thousands of patterns (knight fork patterns, pinned piece patterns -- the list is endless) is what makes you put longer combinations together -- after all, that's all long combinations are: just lots of forced moves involving the tactics you already know working with or against each other. I have made the mistake of going for the long ones, not really knowing the simpler stuff well enough (it's not that a knight fork was beyond me, just that I wasn't good enough to ALWAYS spot any knight fork from a crowded position [just what tactics trainer makes you do], which is something I should have always strived for!), and the puzzles take me an hour and I would only be right like 50% of the time anyway!
The main thing longer puzzles are good for is improving the sheer depth of your calculation and visualization; the thousands of memorized patterns do the rest of the work. Trust me, if you were to do one or two thousand puzzles (just make sure you understand the solution) and you compared how many moves you could spot in your games to before, the difference would be huge. Patterns are what draw your eye to the important moves and thus tell you what to calculate -- more essential than going deep but calculating all the wrong moves and instead failing to some simple 2 move combination.
By the way, that puzzle is pretty cool, but as you said, hardly instructive or beneficial to actual improvement.
What does each add to your game and which makes you a better player? Maybe, easier tactics would be more helpful for blitz and bullet and difficult tactics would be more helpful for longer time controls. Is studying difficult tactics even necessary (for the more amateur level players)? Take a look at this mate in two problem:
I've spent around 15 minutes solving this puzzle which contains a pattern which is not likely to arise in an actual game. I could have used that time to solve 15+ more useful puzzles.