At the end of the day I don't want to discourage you to buy what you want, it doesn't surprise me that the 4k set will have a better picture than the older one it is replacing, so will a newer 1080P TV. Your TV is from 2008 has a contrast ration of 10k to 1 and all TVs have improved dramatically since then.
I am not trying to talk you out of a Sony, but I am trying to save you a few bucks where you can get a similar size screen for less money with better contrast ratio, dynamic range than your current model, but it's your money. To me it is a waste to pay more for 4k, when you will get no benefit from the 4k. I should have waiting to buy mine TBH, but at least the 850C does support HDR.
I have a TON of experience with Sony, if you look at my signature I have the 850C I do use the SAME Sony Apps (Android) that is on the 830C. I have had zero problems, I use Netflix, hulu, Vudu, (I think they got rid of flixter) and have had zero problems with apps. I do think the interface is a little wonky, but once you get used to it, it is easy enough.
If apps are really important, I would seriously consider a Roku or Amazon Fire TV as they work flawlessly, will give you more apps than you can get on the Sony.