Opinions vary on this issue, but here's my take/experience:
I had always used the hook grip (always = 20+ years) because it keeps stress off the callus line at the base of the fingers and is generally easier on the skin.
When I saw some heavy hard style snatchers mention using a deep grip, I started experimenting with it, and it did take some trial and error over time to be able to finesse it so I wasn't painfully pinching folds along the callus line. With the deep grip, there's a degree of goose-necking that's necessary to keep the handle from pinching the callus line and to keep the handle pulling more against the palm of the hand. Otherwise, the "deep grip" ends up being more like overgripping a hook grip, with the stress right at the base of the fingers. Some goose-necking lets you get deeper than that, into the palm
I do find it more secure for heavy bells that are at or above my limit for hook gripping.
However, I also find that the deep grip leads to much more and faster forearm pump. This isn't necessarily a problem with protocols like A+A, where I'm doing 5 or fewer reps per set, resting generously, and alternating arms each set. The sets are short enough so that the forearm pump doesn't build up too much, and there's time for it to dissipate between sets on the same arm.
When I first got the hang of the deep grip, I thought it was great and started to use it for everything. But I quickly discovered that while it helped with grip security, it was counterproductive for grip endurance. The hook grip allows me to keep the forearm much more relaxed and I find it much less fatiguing. As long as my hook grip is strong enough to hold onto the bell, I can stay more relaxed through a longer set and recover faster between sets. I'm sure GS athletes discovered this long ago and that's why GS technique has evolved in the direction it has.
So now I've reverted to the hook grip unless the bell is so heavy that I really need the extra security of the deep grip. And as I get comfortable with a given bell, the more I can transition to a hook grip with it. For reference, I can comfortably hook grip 32kg, and that's the heaviest bell I currently use as a working bell in any normal programming.
For continuous snatching, or programming with more than 5 reps/set, or shorter rests between sets, I use the hook grip. When I started using 32kg for Q&D, starting with a 5/2 rep scheme, I was using the deep grip, but now I've transitioned to the hook grip for that and really all my regular snatch training. If and when I start using 36kg as a working bell I'll probably begin with a deep grip, but I'm now looking at it as a transitional strategy.
Edited to add: I use a mix of cast iron and comp bells and use basically the same technique for both. I generally prefer comp bells, but I have cast iron in my office at work so I use those a lot.
