1. Cutting Words can only be applied against one attack per round (reaction limit). Shield applies to all attacks that may occur before the bard's turn.
2. All of discussion assumes that the bard has a spell slot available (2nd level for Misty Step, 1st level for Shield, so Misty Step has the higher resource cost). Using Cutting Words is an additional resource cost of a bardic inspiration die (of which a bard will have a maximum of 5 only). That extra resource costs may be important in the overall battle.
3. Cutting Words is comparable to Shield against a single attack, though Shield is a guaranteed 5 points impact while Cutting Words could be as low as 1 (or as high as 8, 10, or 12, depending on level). Shield is therefore more reliable to blunt an attack than Cutting Words, but only if 5 points is enough to make a difference, which, as you've pointed out before, isn't certain. Of course, if 5 points isn't enough, Cutting Words is not likely to be enough, either, though it does have a chance of doing so.
This is all dependent on circumstances, of course. Misty Step definitely has more overall utility, but against an unexpected foe that has multiple attacks (not uncommon once you've reached 6th level which is when this discussion comes into play), Shield is the more efficient use of resources.
Looking purely defensively, Shield is a good option. Looking broader at overall usefulness, Misty Step is superior. It will come down to whether the bard thinks they'll be able to survive one round of attacks from an unexpected foe before they have a chance to get away...and how often they think they'll be in that situation.