Can you explain what the difference is between these two kinds of error by the batsman? Why should the batsman in the former case be entitled to recognition for a "great" innings, but the latter not? Both batsman have made errors of equal magnitude. Both errors could have resulted in dismissal but through good fortune didn't.
The degree of error is quite possibly no different. Equally, a batsman who misses a ball by 10cm has made a bigger error than one who gets a thick nick that carries to third-slip. Yet the smaller error results in dismissal.
The simple facts of the matter that I'm trying to get at are not about degree of error, but what is and isn't out. A batsman who is caught and a batsman who is dropped have done exactly the same thing - even though a batsman who's played and missed might well have made a much bigger error. Yet a play-and-miss can
never result in a wicket - a ball being hit in the air to a fielder always should, and usually does, result in a wicket. It's utterly unfair, and inaccurate, to record that a batsman has done something differently when he's dropped and when he's caught.
One aspect which I feel you give insufficient credit for is how a batsman reacts once he's given chances. Chances are (like it or not) part and parcel of batting. A batsman who recovers from giving a chance to score a hundred brilliant runs thereafter still deserves credit for those hundred runs. Take Herbert Sutcliffe, for instance, whose reaction (or more precisely his lack of reaction) to being nearly out was recognised as an intrinsic part of his greatness as a player, and was a major factor in why he achieved the record that he did as a Test batsman.
There is a method for trying to account for this - obviously, someone who gives a chance on 1 and is dropped then goes on to score another 142 before giving his next chance has played far better than someone who gives a chance on 1 and is dropped then gives another just 7 runs later. If you count all chances, rather than just the first one, then divide the number of runs by it (as you under the scorebook average divide runs by completed dismissals) then you get the impression of what you mention - how well a batsman has played.
Yet this method basically suggests that a batsman deserves to have a let-off, with which I don't agree. I'm a bowler, and in my view everything that goes to a fielder's hands at catchable height and speed should be caught, and every decision that should be given out should be given out.