Double OverHand (DOH) grip is most commonly taught to beginners for a couple reasons:
- It feels more natural
- It avoids the feeling of twisting inherent in mixed grip
- It's more important to start deadlifting that listening to complaints about how weird it feels.
That said, there is a limit to how much you can hold that way. You can improve your grip using plate holds, or even simply holding your last rep for 30s at the end. But there will still come a time when you can't use DOH any more.
To that end, you have hook grip and mixed grip as options to move to. Hook grip is stronger than DOH, and it retains the benefits of DOH symmetry. The downsides are you are squeezing your thumb hard, and if you have small hands and a thick bar you just may not be able to do it. Some people are able to deadlift 800lbs with hook grip, but they are exceptions to the rule. Hook grip is most commonly used in Olympic style weightlifting (snatches and the clean & jerk).
Mixed grip is the strongest grip we have:
- As the bar rolls down one hand, it rolls up the other--meaning you can lift heavier things more easily.
- It does cause the feeling of twisting, and to some extent it does cause that.
- Do not flex your arms at all during the deadlift. This is even more important on the suppinated hand (hand facing away from you).
- You do need to switch which hand is suppinated to ensure even training, unlike the other options.
It's not so much a question of either/or, as much as it is when you graduate from one to the other. Many lifters agree that using DOH as long as you possibly can is best. However, when you can't get the bar to budge at all, simply switching to a stronger grip may be all you need to get the bar off the floor.