Last year when I upgraded from my 5D mark 3 to a 5D mark 4 I was in the same position as you and initially I planned to sell the mark 3. However, it has done over 100,000 clicks, the body is all scratched and the paint is worn away. So, although it works perfectly I probably wouldn't be able to get a good price for it and I decided to keep it as a backup. It comes in very useful as a backup to my main camera, but also there are some situations where I carry both of them. For example at sports events I mount a 400mm telephoto on the 5D mark 4 for when the action is far away from me and a 24-70 zoom on the 5D mark 3 for close ups of the players.
Jack questioned the point of having two bodies of the same type, but I prefer to have two camera that are very similar because I now know instinctively where all the controls are, and the 5D series is the best choice for the type of work I do. A 6D would mean making some compromises, and I find the 1D series too big, heavy and expensive - although I might buy a 1DX one day for my sports photography if I win the lottery.
The other big benefit of having an older camera that is so obviously battered and well used is that it makes it much less attractive to thieves, so I use it when I am going somewhere with a high crime rate. I also have a set of old, inexpensive and worn out lenses that I use for this purpose. I am not saying that I will never be robbed in the street but hopefully it is less of a target than my brand new 5D mark 4. Also if someone does take it, well it is a very old camera that I have had for a long time so it would be less of a loss to me.