I’ve got full 6700 on one bike, 5700 gears with 6800 brakes on another and full 5800 on one I’ve just built up.
The hoods are slightly slimmer on the new 5800 but to be honest I can’t tell there’s much functional difference between 5700/6700 and 5800/6800.
I might just have them all set up equally well or equally badly, but the difference in shifting feel is negligible – don’t undertand people’s grumbles about poor cable routing on the 700 series shifters cos I’ve never noticed any particular drag.
And the 6800 brakes don’t feel any more powerful than the 6700 brakes, despite supposed better pad compound.
5800 is obviously a bit heavier than 6800 but that’s probably about it.
Buy what you can afford to wear out and replace, cos the differences to me are minimal functionally.