Pocket holster carry might be said to require even more attention to your immediate environment, as it does present some added difficulty in drawing that a belt holster might not present.
However, pocket holster carry also offers an advantage not usually possible with the belt holster, which is being able to put your hand in your pocket, and grasp the butt, without it being obvious as when grasping the butt of a belt holstered weapon.
This is a trade-off, of sorts. If someone pocket carrying is sufficiently aware of their environment, they can surreptitiously reach into their pocket before it may become necessary to draw and present the concealed weapon. The person carrying the belt holstered pistol tries to grasp their holstered handgun, it's generally quite obvious.
Yes, trying to drawing while moving can be difficult, regardless of carry method, but trying to remove a handgun from inside a pocket can usually be more difficult than trying to draw from a belt scabbard. This is where the aware and prepared person, using pocket holster carry, may be able to get "ahead of the curve" by being able to have already grasped their weapon before the need for movement becomes necessary.
It's all a compromise, not matter how you look at it. What offers an advantage in one set of circumstances may not be advantageous in other circumstances.
I thought I remembered Mas writing an article some years ago discussing this, where he timed himself drawing and firing from both belt and pocket holsters. (It might've been another writer of the time, some years ago.) Anyway, when he was able to reach inside his pocket and grasp the gun before he had to draw, which was done using a hand-in-the-pocket gesture that would appear normal to most folks (as opposed to someone resting their hand on a belt-holstered gun), he was faster in getting off his first shot. Advantage to pocket holster carry.
Driving, or being otherwise seated (like in a movie theater, at an office desk, etc) can introduce another layer of difficulty for the pants/jeans pocket-holstered gun, but not, perhaps, the jacket pocket-holstered gun. Oh well, TANSTAAFL.
I spent many years also using pants & jacket pocket-holster carry, at the same time I was wearing belt holsters, when working at our range as an instructor. It was something I wanted to frequently practice, so it became at least second nature, if not first nature.
In some instances where I was wearing a heavier layer of outer garments, such as a raincoat over my sport coat, being able to have my 649 Bodyguard snub in my R/H outside raincoat pocket made it very easy to sometimes grasp the butt of the snub without it being obvious, or appearing as anything other than an ordinary gesture of keeping my hands warm. It also made it easier if I needed to access that snub while seated in the unmarked car, versus trying to reach for the belt gun.
As with many other things in this realm ... it depends.