Cross draw does not conceal as well as a strong side because it's worn farther to the front while a typical strong side rides behind the hip bone. If you slide a cross draw to the rear it conceals about as well as a strong side, but it's inaccessible for a fast draw.
This puts the properly worn cross draw up in a more exposed position that's harder to conceal.
There's lots of strong side inside the waist band holsters, not so many for cross draw.
The advantages of the cross draw are better comfort and access while seated and access with the off hand if your normal gun hand is unavailable for some reason.
One big advantage of a cross draw is that of the appendix carry..... speed.
To draw a strong side you have to use your gun hand to sweep the coat out of the way and keep it out of the way while you draw the gun.
This is a problem some older cops solved by sewing a small lead weight into the tail of the coat so the coat tail would swing away if you did a fast hip duck to the side.
The appendix and cross draw can be very fast because you use your off hand to open the coat.
Also, if you have your hands in a forward or clasped position, your gun hand is RIGHT ON the gun.
All you have to do is lift the coat and your hand is already on the gun.
One of Jeff Cooper's shooting friends was a narc cop who adopted the habit of clasping his hands in front in a none threatening hippy method.
If needed he virtually had his gun already in his hand.
I think it was famed Colt employee John "Fitz" Fitzgerald who developed a fast cross draw technique that eliminated sweeping someone else, swinging the gun past the target, AND limited a gun grab.
What he did was to rotate his gun side away from an attacker as he grabbed his gun, then rotated his body back toward the attacker as he lifted the gun up out of the holster.
As the holster moved away his hand lifted the gun and it was pointed right at the attacker.
This looked like he was doing The Twist dance.
The only problem with this is like all special techniques, it can't work all the time under all circumstances.
This is like the old formal FBI technique of lifting the left foot, moving it a couple of feet to the left, then just squatting as the gun was drawn, holding the left arm across the chest to "block a bullet".
Jeff Cooper and Sheriff Jack Weaver ended all this with their "Shoot as you are" method.
That method teaches to just get the gun out and into action from no matter what position you're in and forget any special stances or techniques. If you're half way out of a car or jumping over a wall you can't use some special stance.
The hazards of a gun grab from a cross draw are no worse then a rearward grab from a strong side, and even less then from a horizontal shoulder holster.
The main reason the cross draw fell from police favor was because it was considered to be more dangerous on a shooting range during training while other shooters were on either side.
These days you're seeing a lot more cops wearing horizontal shoulder holsters, which begs the question "What do they train with on the range"?
The cross draw definitely has a place as a CCW holster, but you have to accept that an outside the waist band type won't conceal as well as a strong side.
If you can work with that, or you spend a lot of time seated, especially in a vehicle, it's the preferred type for both comfort and accessibility.
Some holster makers actually make special "Driving holsters" for bodyguards and other people who drive a lot.
I very much like the cross draw and make my own.
Here's one for a S&W Model 66 and another for a Kahr Arms K9.
These have a reversed design with a forward seam to act as a sight channel and the smooth folded rear is more comfortable if it digs into the top of your leg. In addition, the folded rear makes for a much smoother draw since the gun can slide out faster without dragging on a welt.
The Kahr holster has my "half and half" trigger guard design.
As a form of cross draw, these days I carry in a Blackhawk Urban Carry fanny pack.
I installed a Kydex cross draw holster. Again, the front seam acts as a sight channel and the folded rear allows the gun to slip out without drag.
This type of fanny pack is also known as a "5-5-10" because it allows drawing a gun and firing 5 shots in 5 seconds at 10 feet.