My full time job is a wedding photographer, I currently have a couple of 5D3's and a 5D4, before the 5D3's I had 5D2's and before that a 5D1, I also had a 40D but started with a 300D, I also have a 1DS-MKII which doesn't get used due to the low ISO capabilities but does take a lovely image.
Owning these full frame cameras (apart from the 40D & 300D) over the last 15 years, the key reason for me to upgrade has been the ISO and the focusing system, for AP the focusing system is not so vital but ISO is.
I can say anything before the 5D2's would have a lot of noise around and above 1600iso, a 5D2 would shoot with a some noise at 3200iso but can be improved in software, the 5D3 is fine at 3200iso with a little noise and can be pushed further, the 5D4 I regularly shoot at 6400iso for first dance images and now and again push it to 12800iso, again some noise but not too much of a problem with software.
Yes the 5D4 is best of the bunch but it was the smallest advancements over the previous upgrades, its better than the 5D3 in lots of small ways but not one big way. So if you want to get a good camera at a great price (around £1000 or less) that can handle decent ISO I would say go for a low shutter count 5D3, saying that one of my 5D3's has around 400,000 actuation's while the other is getting towards 300,000, both on the original shutter!
Of course all this is irrelevant if you want to stick with crop sensor based cameras but in general full frame bodies handle noise better..