There are situations where blade ward is the most effective defensive technique, but most of the time simply taking the Dodge action is actually better. If I recall how it works, blade ward is more effective than Dodge when you are being targeted by non-magical slashing, piercing, or bludgeoning weapon attacks, and your opponent has greater than a 50% chance of hitting you. At any other time Dodging is better. Since your opponents rarely have a greater than 50% chance of hitting you, Dodge is usually better.
That's a pretty strong claim to knowledge about various tables. If I made that claim I'm not sure how I would defend it, so I'd rather say "if" than "since".
Reasons to use Blade Ward over Dodge:
1.) You're a squishy AC 11 wizard.
2.) You're a semi-squishy AC 13 + Shield spell wizard who is being targeted by, say, a Nycaloth (+9).
3.) You're a a semi-squishy AC 13 + Shield wizard who is being grappled by a giant ant/crocodile/whatever and therefore cannot benefit from the Dodge maneuver by RAW.
4.) You're a warlock with Armor of Agathys up/wizard with Fire Shield up and you would rather take half damage while inflicting full damage all the time than take full damage half the time and inflict full damage half the time.
5.) You're an Eldritch Knight with War Magic.
6.) (Arguable) You're facing a threat that cannot be dodged, e.g. you're falling to your doom and hope that Blade Ward will save your life if the ground counts as a bludgeoning weapon.
7.) You use an alternate initiative system like Speed Factor Initiative which makes Blade Ward sometimes last long enough for you to get an attack off while it is still up.
8.) You'd rather face two DC 10 concentration checks than one DC 20 Concentration check.
9.) You're trying to avoid death from massive damage.
That's all I've got. None of these situations have yet occurred in any of my games[1]; but I still find them compelling enough that I often try to learn Blade Ward if I have some extra cantrips free. It's insurance in case I ever get into any of these situations.
[1] Well actually, #7 does hold when I DM... but I don't get to make and use PCs in my own games, so Blade Ward isn't really an option still.