They both have good "drop-hand" effects that disrupt common plays. They are also both Level 1 Monsters, meaning that they could be used for Synchro Summons or just Set as a defense.
While Effect Veiler can stop almost everything that D.D. Crow can stop, D.D. Crow stops the things that it stops better, if that makes any sense. Basically, D.D. Crow gets rid of the problem, while Effect Veiler just stops it, generally.
D.D. Crow removes Monsters from the Graveyard, so your opponent can't just get them later with another effect. It also hits stuff like Treeborn Frog, Fishborg Blaster, and Pot of Avarice, which Effect Veiler does nothing against.
On the other hand, Effect Veiler stops effects that don't use the Graveyard, like Machina Gearframe, Monarchs, and Gladiator Beast Gyzarus. Unfortunately, Effect Veiler only works during your opponent's Main Phase on their face-up Monsters (Book of Moon can stop it, basically).
There are other aspects of these cards that are often ignored. Effect Veiler is a Light Tuner and gives access to Ancient Sacred Wyvern, in addition to all generic Synchro Monsters. D.D. Crow is a Dark non-Tuner Winged Beast. It can be used for Icarus Attack, which is fairly common.
D.D. Crow can also be helpful in decks with too many Tuners. There usually aren't decks like that, but Scraps and X-Sabers can fall under that category. It would often help those decks more to have a non-Tuner rather than another Tuner.
However, the most important things to consider are the match-ups your deck is weak against.
Against Machina Gadgets, Gladiator Beasts, and Gravekeeper's, Effect Veiler is almost always the better option. D.D. Crow can work on some of the cards that those decks play, but it's more situational. This is the same case for Perfect Herald, for those OCG players that have to deal with the new Lost Sanctuary Structure Deck.
With X-Sabers, Frog Monarchs, and (Quickdraw) Plants, Effect Veiler and D.D. Crow can be equally useful. There are some situations where Effect Veiler is better (XX-Saber Boggart Knight, Monarchs, Ryko), and there are some situations where D.D. Crow is better (XX-Saber Faultroll, Treeborn Frog, Pot of Avarice, Glow-Up Bulb, Spore).
Against those decks, though, D.D. Crow is better than Effect Veiler when they use some sort of effect that involves the Graveyard. While Effect Veiler stops Debris Dragon, D.D. Crow removes the Dandylion from play. That's HUGE in that match-up, since (Quickdraw) Plants rely on Dandylion.
So, the ultimate deciding factor is whether or not you can give up the increased utility of Effect Veiler to play a more effective counter to Graveyard-dependent decks. Basically, if your match-ups against Machina Gadgets and Gravekeeper's are good, then you should be playing D.D. Crow over Effect Veiler, unless you want/need the Tuner for Synchro Summons. Either way, you're generally not going to summon Effect Veiler when it can protect you from the hand.