Thanos was shown to have the Reality gem in the Cosmic Powers Unlimited series (issue #1) when he summoned Captain Mar-Vell. I'm pretty sure he never used it in the Infinity Watch series. He brought it out during the Infinity War, but it was a fake to trick the Magus.  

castleking answered the Infinity Gauntlet question very well.

Well it is an established comic book concept that "The path to hell is paved with good intentions" and we have seen recently how Adam still has the capacity to turn into Magus, a threat to all realities not just his own. I'm sorry for this bit of knit picking but Thanos was actually tasked with destroying half the population of the universe not just half the population of Earth. 
 
That Thanos was in the process of/had destroyed truly vast numbers of people was never Eternity’s issue. The objection was that with the gems Thanos was omnipotent and would replace Eternity. With this in mind The Living Tribunal chose not to get involved, he told Eternity his reasoning. As castleking said Thanos was in fact carrying out a very old cosmic law “survival of the fittest” rather than breaking any cosmic laws. Perhaps that Adam had no intention of assuming the role of an abstract cosmic deity was the problem. That he planned to co-exist with Eternity yet through his power impose his will on that entity, a tad redundant.

In short maybe the difference was that Thanos never alluded to any plan of using his power to arbitrate wrong from right while Adam very much did.

As another thing to keep in mind is what the Living Tirbunal is and how far above human comprehension and logical process it supposedly is. It doesn’t have to make sense to humans to be obeyed and we got a great new comic out of it.