I didn't get any 'book larnin'" in my AOW class that I didn't have from OW (actually, in my AOW class there was no 'class' at all, just doing the dives with the instructor and the other students). What I got was dive experience when I had very little (I still have very little, but slowly getting more) -- 6 additional dives with different experiences on each one (drift, night, deep, wreck, navigation, something else I don't remember). At the time I had only a dozen or so dives under my belt (including the OW checkouts) so this was a big deal. If I'd had some friends who were experienced, safe, divers, I could have gotten the same experiences without the class, with them, but I didn't. So my first time below 60' I got to do with an instructor and a few other students. Made me feel more secure. The card allows me to go on some shop-organized dive trips (recent one had numerous dives below 80' and required AOW & NITROX to go), but no substitute for experience and (for me anyway), continued training. What makes diving between 60 - 130' safer? Experience diving between 60-130'. And an AOW class is one way to start getting that experience. So there's the card, which is one thing, then there's the experience and training, which is another. These are separable.
A different example than depth: I've been uncomfortable with my trim -- lots of side-to-side rolling. Never addressed in OW or AOW. Knew it was part weight amount and distribution and part skill, but how to deal with it? I didn't have a dive buddy willing to spend a dive day working on this so I decided to take a class. Could have taken buoyancy & trim, but decided instead to kill multiple birds, and since I had the opportunity, I took Cavern instead. Why (well, other than because caverns are cool)? Because I know that buoyancy & trim are critical in the overhead environment, plus the course would task-load me underwater. So, after a 2-day course I have much improved buoyancy & trim (the instructor spent time with me adjusting the BC and weights), plus I've had to air-share, follow a line, and find a lost line all with a blackout mask on. Will I ever have to do that real world? Don't know, but I do feel just a tiny bit more confident that if I ever have a real problem underwater I'm less likely to panic and am more likely to think it through because I've had to problem-solve underwater (admittedly it easier when I know there's an instructor right there to pull me out if I can't find the line). Experience and training give skills and confidence; the card gets me on the boat where I can get that experience.