Most grip tools are single handles. There are many advantages to this. For one, competitive grip lifts like the block lift, hub lift, and rolling handle lifts are all done in competition using one hand. If you wish to compare yourself against others, then you will want to lift in the specific way others are testing their grip.
Another advantage to working single-handed lifts is that it allows you to target your weak hand or strong hand. If you just want to lift maximum weight, you can focus only on your stronger hand. Arm wrestlers do this all the time, (most of them don’t train both arms).
If you want carryover to other strength exercises and balanced muscular development, you can shore up the strength in your weaker hand by selecting the right weight to train with; That means less weight than your stronger hand.
Training with one hand at a time also allows you to fix technical issues with either hand better. If you’re training both hands at the same time, your stronger hand can dominate and pick up the slack for your weaker hand; this isn’t necessarily something you may want.
Single-handed grip lifts also allow you to focus your neural output into that one hand better, maximizing performance. Stronger sets always = getting stronger!
With all these advantages to single-handed grip work, are there any advantages to two-handed grip exercises? Definitely. The most obvious advantage is that it saves time. Another advantage is, again, related to specificity. Some grip lifts are two-handed lifts! Check out the axle deadlift (a fat bar with no knurling).
If your goal is to increase your grip strength for deadlifting or hang from a pull-up bar for a very long time, then it’s essential to train these specifically. Double overhand deadlifts and dead hangs from a pull-up bar are fantastic exercises for your grip. Don’t forget you can add weight to make the dead hang exercise super challenging to hold for more than a few seconds: that will maximize your strength instead of your stamina.
Two-handed and single-handed grip exercises should be adapted to your goal; whether it’s to get super strong for competition, carryover to other lifts or sports, build grip stamina or build muscle in your forearms: I feel like grip training and integrating grip exercises into your existing routines is best done by using a mix of two-handed and single-handed grip exercises. Don't forget, you can also use x2 single-handed grip attachments for bilateral exercises! Now we're getting creative!
Start with your goal in mind and consider what mix of two-handed and single-handed grip strength exercises can get you there!