For the benefit of those who find this thread (like I did) after searching on either model number.... I have a UN40ES6150 (Costco model) and can confirm the "clouding" or "flashlighting" anomaly of the screen. But the configuration options are more extensive, and using this site's review/calibration settings, have what I deem to be really great color authenticity. The SmartHub and various apps are still being updated some 2 years after purchase, which is notable. Compare with my Panasonic BDT210 player which hasn't had new firmware or Viera app updates in years. Though serviceable, the Netflix app is showing its age.
A friend bought a 50EH6000 recently, and since she owns a Chromecast, has less need for the apps. After configuring, the picture looks great. I only watched one movie on it, so I can't comment on her set's quality with a variety of movies.
Bottom line, the ES6100 series seems to offer many more features and configuration options while sacrificing some image/picture quality, while the EH6000 is less "feature-full" while offering a better backlight configuration. GIven the choice today, I'd get the EH.
As others have mentioned, test in the store to suit one's test. LCD TV Buying Guide's calibration settings guide
may be a good baseline for assessing the TV before buying. (Expert users here caution that calibration can vary from one consumer unit to another, so those settings can't guarantee the same quality in every single EH6000.)