I am starting the cross draw fan club. IWB cross draw carry rocks!
For me it overcomes the main issue of concealment: keeping the gun in an easy to access, secure position without paralyzing regular movement.
I think it's not so much that cross draw carry is any better than strong side carry for any tactical reason, but rather a strong physiological one. Typically your body follows your dominant hand, and in my case I strongly favor the right side.
There's a test I learned a long time ago to determine which eye you should shoot with. You hold your hands up such that your fingers end up in a diamond with your thumbs and index fingers touching each other. You then look, with both eyes open, at something across a room that fits in the little box you just made, say a lamp.
Close your left eye, open it, then close your right eye, and open it.
When I do this test, when I close my left eye, the picture does not change at all. None. When I close my right eye, whatever I was looking at is no longer visible, obscured by the opacity of my left hand. In essence what I see with my right eye is nearly identical to what I see with both eyes. I am very strongly right eye dominant.
Now combine this tendency with being right handed in the first place, and I think I create the poster child for someone who really needs to train up their left hand! I've worked on it a little bit, but it's an uphill fight!
Where I'm going with all this is that I suspect I am severely dependent on the motion of the right side of my body, and this is why I suspect placing a gun on that side completely paralyzes me. All of my motion follows that dominant hand and eye.
Cross draw carry eliminates all of this, and in fact I speculate now that I'm starting to get slightly better adjusted to the whole carry concept, I think it's starting to have something of the opposite effect of paralyzing strong side carry. It's beginning to feel like it belongs there.
Another thing I have found is that although it still prints noticeably, since my left side stays still more often than my right side, it helps with concealment for some reason. I think it's because the butt of the pistol is facing the other direction. I just spent a week as a guest in a relative's house, and since I was in a private residence and spent the whole time on private property, I figured I'd practice carrying. No one noticed, and these are gun savvy people. Even with the printing it worked, and I wasn't using a cover garment beyond a T shirt.
Presentation has taken a bit of getting used to. What I have developed is I will first use proper techniques to insure the weapon is unloaded, confirm it is unloaded and that there is no ammunition in the room, and then practice drawing it, ending up in the ready stance. It's a little more complicated than that actually - see the draw described in Gabe Suarez's The Tactical Pistol for a better explanation with correct and descriptive language of what I'm working on. It is getting smoother however, and I've long since stopped having to look at the gun to draw it. I want to get where it's a reflexive draw like producing a knife.
I think overall however the concept of keeping something you probably won't use everyday (or hopefully ever!) on the side of your body that doesn't groove and move so much is one that everyone should consider. I can't believe it's not the dominant form of carry!
No one at the range likes the crossdraw concept at all however. I am constantly told how unsafe it is by people whose opinions I don't weigh too heavily. How is it any different, honestly? The one problem I see with it is that it makes it difficult to use space to your advantage. With strong side carry you can use the idea of "space" transitions much more easily. I would also speculate that the fact you are required to reach across your torso basically means that at some point in the draw stroke, you present your aggressor with the largest possible target, but that's just me nitpicking.
My theory is this: I think the relative unpopularity of this method may derive from the fact that most people aren't quite as dependent on one dominant side of their body as I am. I hope this is true. Even a cell phone on my belt on my right side feels like a brick, and a gun in concealment just constantly gets in the way. It's as if someone stuck 20-30 large needles in me right in that one spot. I wouldn't wish my frailities on anyone else, this one not withstanding. I'd speculate the average person is somewhat closer to being ambidextrous and not as sensitive to something poking their strong side. But there's enough people like me far enough along the spectrum that keeps the cross draw concept alive.
As for me, I'm becoming a believer in 10'o clock carry, and that's a concealed carry solution.