Thought I'd throw in my two cents here, since I've always ridden 7700, 7800, 7900, and now 9000 (both mechanical and Di2) but set up a couple bikes with 6800 (and one now with 6870/RS785) after doing 6500 and 6600 (skipped 6700) and put a good number of miles on them as well.
First, I think that observations from older generations of either Dura Ace or Ultegra are not informative. Ultegra has taken some great steps forward and both performance and durability are markedly improved relative to the group's predecessors and also relative to 9000/9070. So I'd discount people comparing from older generations.
Second, 6800 and 9000 both have weak spots. The front derailleur on 6800 isn't as nice as the 9000. The 9000 cassettes aren't trustworthy like the 6800 ones (and 6800 has some combinations that aren't available in 9000). The 9000/9001 shifters have cable wear problems that it appears 6800 doesn't have, but instances of cable wear are spotty and many people have no problems at all while others have incessant issues (I haven't had any problems with either 9000 or 6800). But for the most part, the parts come down to small cosmetic differences, a fair bit of weight, and in some cases a perceptible but very small difference in operation.
The 9000 front shifter does an outstanding job on any crank and any chainring combination including non-approved ones (I'm riding 39/50, 34/42, and 36/46 Shimano rings and 36/46 Praxis rings with no problems at all). The 6800 front shifter does really well with most approved ring combinations and with most Shimano cassettes but peak performance is with 34/50 rings and 28- and 32-tooth Ultegra cassettes. It doesn't do as well with 11-23 Dura Ace cassettes, with 7950 cranksets, with Rotor rings or with other specialty brands. The 9000 does a better job overall. But both fade compared to how either 9070 or 6870 shifts.
The 6800 and 9000 bottom brackets, the cranksets, the brakes are all pretty much interchangeable except for weight. I've put enough dirty rides on both and haven't seen any problems with the 6800 finish -- if anything, it's tougher than 9000 (7950 cranksets were a lot tougher cosmetically in my experience than 9000 ones). The 6800 chainrings don't have all the detailed ramping and pinning that the 9000 ones do, but as long as I'm on standard approved ring combinations I see slight difference between 6800 and 9000 and nothing at all after going to 6870 or 9070. I'm not sure the 6800 brake blocks are the same as 9000, and thought there might have been better blocks on the 9000, but I swapped up the brake blocks on the 6800 and both versions were superb and indistinguishable.
The 9000 hubs go for a couple years and still act like they're brand new. My oldest 6800 hubs have been through two long wet winters and loaned out for lots of cross, and still feel like they're new. I haven't seen any sign at all that 6800 hubs don't have practically lifetime durability. The 6800 free hubs seem like they don't have the ratchet count of the 9000's, but it doesn't affect the riding and the 6800 free hub shells are definitely more durable than the 9000 ones. The quick releases are identical except for a little bit of extra finishing and shaping on the Dura Ace.
In short, Ultegra has become a better and better group and closed much of the historical gap to Dura Ace. Current Dura Ace is an improvement over 7900, but that's mostly in small increments except for significant improvements in cable action. When we go to 6870 or 9070, it's a push button. I've swapped pieces back and forth and not been able to sense a difference between any of the drivetrain components with either 6870 or 9070. You can feel slight differences in the levers, but that doesn't mean the 6870 was a problem in any way -- it's just aluminum versus carbon fiber, or a slightly bulkier shape instead of thin. I'd be hard pressed to pick between 6870 and 9000, but most of my equipment has 9070 now and I'm gradually going entirely Di2. It really is that good. I'd use 6800 in a heartbeat on any bike. I have no concerns about durability or about quality of performance with any of the four groups, and I couldn't quite say that about 6500 or 6800 or frankly about 7700 or 7900.